The best alignment for most clerics, in most campaigns, is probably some flavor of Evil, oddly enough. There are two reasons why:
Infernal healing is an Evil spell, and one of the very few aligned spells that doesn’t have a precise analogue in other alignments. It’s also the best healing in the game—a wand of infernal healing will heal more hp per gp than any other option in the game (and using gp is always better than using spell slots).
Most campaigns face Evil foes, and at high levels, the most evil foes—fiends—often sport at-will blasphemy. Many of these do not have much flexibility in this regard: blasphemy is a spell-like ability that they have, and they don’t usually have dictum even if they’re also Lawful or word of chaos if they’re also Chaotic. And if you are Evil, their blasphemy does nothing to you, which is a big deal because blasphemy can be devastating.
And while blasphemy is—by far—the biggest concern here, at lower levels there are also other aligned effects that follow a similar pattern: fiends usually have the Evil effect, not the Lawful or Chaotic effects, and being Evil makes you immune.
But these advantages are very small and/or circumstantial:
Neutral clerics can still use infernal healing. It may, depending on the GM’s ruling, be an Evil act to cast infernal healing, which the GM may rule will eventually cause someone to slide to Evil even if they didn’t start there, but you’ll have to ask your GM about that.
For Good clerics, a wand of cure light wounds is nearly as good, and channeling positive energy provides some supplemental healing that probably makes the difference close to a wash most of the time. (There is a celestial healing spell, but it is terrible, so just use cure light wounds.)
This point only applies to “most” campaigns, where you can expect primarily Evil foes. If that doesn’t describe your campaign, then it doesn’t apply. If your campaign focuses on foes of a different alignment, then matching that alignment may be best. If your foes’ alignments are fairly uniform, then there is minimal advantage to any one alignment versus any others—most aligned effects come in all four flavors, so it doesn’t really matter which ones you have.
Also, most aligned effects aren’t terribly scary or worth worrying about. Blasphemy, and its counterparts (dictum, holy word, and word of chaos), are really the main extremely dangerous aligned effects, and those only happen at very-high levels. Smite is fairly dangerous, since it it can massively improve the user’s accuracy against you and give them a respectable damage bonus to boot, but smite is usually rarer in most campaigns. I’m having trouble thinking of any particularly worrisome aligned effects after that.
Finally, there’s a flip side here: even if you are an Evil cleric, facing Evil foes, and enjoying protection from their blasphemy, remember that you can’t use blasphemy against them either, and holy word isn’t allowed to you. You would probably want to be either Lawful or Chaotic as well as Evil, so you can safely use dictum or word of chaos on them. This again applies to lower-level effects, but for the most part you could just skip the aligned effect altogether and go with something unaligned; it will usually be better.
You’ll note that neither of these points really has anything in particular to do with the cleric class. Channeling positive energy more-or-less cancels out the disadvantage of not being able to cast Evil spells—that is, not being able to cast infernal healing, since that’s more-or-less the only one you should particularly care about. So even the one thing that the cleric class does touch on, it does so in a way that mostly cancels out. This is because the primary cleric class features that key off of alignment are weak.
Aligned spells almost-always come in all four flavors, so it doesn’t really matter which ones you have and use. Infernal healing is literally the only exception I can think of.
For that matter, for most aligned spells, there are unaligned spells that are largely superior anyway. Only the blasphemy/dictum/holy word/word of chaos cycle is especially notable.
The cure and inflict spells are awful, and basically should never be used
The only healing spells in the game that are really worth using from your spell slots—rather than from a wand—are
stabilize (because it doesn’t use a spell slot, and can handle an emergency), and
heal (because it heals massively more than any other healing spell, and also covers most status effects at the same time).
For damage, literally any other damage spell will be better than inflict wounds at the same level.
Channeling positive energy is a decent amount of supplemental healing, but you still want the wand for most of your healing. Channeling negative energy can allow you to build up an undead army, but you need to put a lot of work and resources into that. Which one is better depends on whether or not you’re going to put the work in to getting the undead army—out of the box, positive is better, but with investment, negative is better. (Don’t invest in channeling positive energy; basically none of the effects are worth it. Just enjoy what you get for “free.”)
The alignment domains are all pretty bad. I’m not 100% sure about the subdomains, there might be some decent stuff in there, but even if there are, there’s also plenty of good stuff in unaligned domains, so you aren’t really missing out that hard.
About neutral clerics
As Ben S.’s answer points out, you are incorrect about how the “one step” rule works—effectively, it doesn’t offer diagonal steps on the alignment chart, so “a diagonal step” is actually two steps.
Moreover, because the most potent aligned effects are blasphemy et al., and you really need to have that alignment in order to use them (you are not left out of the area of effect, and will suffer from it if your alignment doesn’t match), neutral clerics are actually in a lot of trouble on the alignment front—you’re vulnerable to all four, and can’t use any of them safely. (Obviously, this only applies at the very-high levels where those spells are found.)
Still, combining channeling positive energy with infernal healing is something; you have the most healing in the game. But all that really does is save you some money on buying wands of infernal healing, which you shouldn’t be going through so fast that the expenditure is really a problem. I wouldn’t assign much value to it, myself.
“But wait, evil clerics can’t get spontaneous cure!”
This answer has drawn numerous comments claiming that a good cleric’s spontaneous cure is important to survival, evil clerics must now prepare cure spells since they lack that feature, etc. etc. This is an understandable sentiment: that is how the game depicts clerics, casting cure spells round after round. Certainly, if you’re going to be using cure a lot, casting it spontaneously is the way to go, since that allows you to prepare any other answers you want. So the ability to spontaneously cast cure spells is supposed to be a large advantage; it’s described as such and it’s very likely that its authors (going all the way back to Wizards of the Coast’s original implementation) intended it to be such.
But it’s just not true. This is the “trap” of the cleric class.
I call it a “trap” because the description of the cleric class leads you to thinking it’s the right way to play the class, and because once you start down that path, you can get stuck there.
So what’s the problem here? The cure spells are bad. Their numbers are just too small, which means you need to combine them with channeling positive energy, you need to get magic items and take feats, all to try and get them into a good place. And all of those options that you can get are scaled based on the cure spells, so you spend a lot of gold, or a nearly-priceless feat, on small boosts to what you can do. And you spend all your time trying to keep up with cure spells that are never going to cut it.
(Note that almost all of this analysis is specific to cure spells—the heal and mass heal spells do not follow the same trends, because those spells have very good numbers, not to mention powerful effects beyond hp healing, and so are legitimately strong choices. But those spells are also unaffected by alignment, since the good cleric’s ability to spontaneously convert prepared spells into cure spells doesn’t let them do the same for heal or mass heal. You just have to prepare those, but they’re easily strong enough to be worth preparing. They are also strong enough not to need extra feats or magic items to boost them.)
In combat, the most valuable thing you have are actions. You need to do as much as possible to turn the tide in your party’s favor with every single one, because you will not get many. Characters can do a lot on their turns, and so can the creatures they fight. A typical Pathfinder combat is decided in 2-3 turns, tops—there might be mopping up to do, or a retreat to manage, but whether or not you are ultimately going to win is usually pretty clear after that point. That should make you suspicious of the relatively low numbers on cure spells—and you’d be right to be so.
It is very difficult to cure someone of more damage than a typical foe of the same level can do in a single attack. Plenty of characters and creatures can have multiple attacks right from 1st level, and just about everybody who cares about attacking has them by 8th at the latest. So when you spend your turn casting cure, your turn has been spent undoing less than an enemy turn’s worth of damage. That’s a losing proposition.
Moreover, the cleric is a formidable fighter—which means they can easily deal more damage than they can cure, particularly if they build for it. And the cleric spell list is very, very good—which gives you lots of other options for protecting your party or dealing with enemies.
So you could inefficiently cure, and spend an entire turn undoing a portion of an enemy’s turn, or you can be more proactive, and do something that directly eliminates or mitigates threats, either by limiting enemies’ ability to attack or by enhancing allies’ defenses (or indirectly, by buffing allies’ offense so they can limit enemies’ ability to attack by killing things). In pure numbers, the latter approach saves vastly more hp than the former can heal in the same amount of time. Finally, remember that healing is itself inherently inefficient—you need to wait until the enemy has dealt damage in order to heal it. That means you always risk the enemy killing someone in between—not good.
All of which means, when your few opportunities to determine the outcome of a fight come up, it is going to be very rare that a cure spell is the best possible answer. So why do people swear by it? Because they’ve built clerics who are focused on cure spells, and now they struggle to do much else. The cleric is extremely versatile, but it is possible to get yourself into a hole with one—and focusing on cure spells is a good way to do that, because cure requires so many resources focused on it to keep up. It’s entirely possible that these clerics can’t do better than cure, and that without the contribution of a fully-powered cleric to protect people or power through the fights faster, in-combat healing becomes necessary. But that’s a losing proposition every time it happens, and it is far stronger to build a cleric around the idea that it’s not going to—that we’re going to get through this fight, and then heal. At which point the wand of cure light wounds or wand of infernal healing is the way to go.
This actually kind of reflects a “thing” with Pathfinder, and D&D 3.5e before it: the things that the authors thought were good, often aren’t. Because they thought they were good, they were conservative with them. Oftentimes, too conservative—as with cure spells. Most direct-damage spells are in a similar boat, for the record (though their numbers aren’t nearly as bad as cure or inflict spells’). So very often the best options aren’t the ones that are presented as the best options, because those options were reined in and other options—not perceived as strong—were buffed to make them seem more appealing. This kind of over-correction is found throughout both systems.
