Races barely matter
The racial bonuses are small and simple in the overwhelming majority of cases. I do not recommend worrying about them much. I would recommend general houserules regarding the half-elves and half-orcs (which are curiously and decidedly weaker than their full-blooded parents), but that’s not really an issue for a new player and not super important besides.
Just avoid Racial Hit Dice and Level Adjustment. Again, this is something I recommend for all players, not just new ones. They’re poorly designed and skew the game in bad ways.
In the few cases where Human is not the absolute best choice, it is always at worst the second- or third-best choice. For anything. And it has no ability score penalties, so it is a rather safe default answer. But really, any race the player likes is probably best. There are few “traps” in the racial choices.
Class is massively important
Classes form basically everything in 3.5; there is not much system left outside of classes. Unfortunately, not every class was made equal.
The organization of this post is going to be removing certain “types” of classes as unlikely to be the best choice, leaving with a smaller subset of 3.5 that consists of classes I really like for this. I’ll explain why I remove each candidate that I do. Skip to the bottom to just see recommendations.
Do note that classes and races do interact with each other. The most important thing is that you should not choose a class that relies primarily on a score you have a racial penalty to; having a bonus to that score isn’t so important, but not having a penalty is fairly important. Choosing a similar class that uses a different score, or choosing a similar race that doesn’t have that penalty, are frequently both options.
Avoid classes that have no special subsystems
Classes like Fighter, Monk, and so on, tend to be A. low in power, which gives a new player less margin for error, and B. their options are few, far between, and critical. While at first glance, it appears that having few options is good for a new player, these classes tend to make each decision that does come up incredibly important – and difficult to answer.
These classes are almost universally unforgiving, too: once a choice is made, it cannot be unmade.
The obvious example of this is the Fighter with his Bonus Feats. There are a lot of feats; even in Core, there's quite a few. Most of these feats are traps: options that are decidedly weaker than others, to the point of being almost useless. Every +2-to-two-skills feat ever written is in this category, for example. The +2-to-a-save feats are largely in this category as well. Dodge, Mobility, Spring Attack, Whirlwind Attack: all awful. These feats encourage players to make mistakes, because the book does not give any indication that they are weak.
Indeed, it seems likely that Wizards did not recognize this imbalance – but at least one of them claimed that “that was the plan all along!” that Wizards intentionally wanted to reward “system mastery” because it had worked so well in Magic: The Gathering. I find this claim dubious and likely just a (really weak) attempt to save face, but the claim was made.
Finally, subsystems are simply too important to 3.5 to ignore. They’re an aspect of the game that a new player should be comfortable with: it is a bad idea to hand-hold a player into a class without one, and then leave them there. Many players wind up with the idea that classes with subsystems are much more complicated and difficult to play than they are, and it limits them in what they are willing to play.
Avoid classes with too many options
This kind of goes without saying: sorting through the entire sorcerer/wizard spell list is just a lot of work. Finding appropriate wild shape choices, and statting all of them out, is also a lot of work. Playing a competent Artificer apparently requires a degree in accounting.
This is probably obvious to everyone who has considered the problem, though.
Avoid classes with rules that are complicated, counter-intuitive, or fiddly.
Basically, anything that’s difficult to explain or to remember. Ideally, you want something that is pretty close to: here are some powers. Pick a few, and then you can use them.
Incarnum is the worst offender here; even experienced players often get confused on some of the details of that subsystem. Much of the problem has to do with Magic of Incarnum’s incredibly poor layout and organization.
The Artificer comes up again here, since the item-crafting rules are a mess.
Don’t want the player paralyzed with super-critical resource choices
Resource management is an important part of 3.5’s system, but a new player is not going to be able to judge well when a resource is worth using. This can lead either to “nova’ing” and the player being out of resources in later fights, and therefore struggling to contribute, or refusing to use resources even when appropriate. Or someone else from the group telling them every time they are supposed to do so, which isn’t any better.
Tight limits on per-day abilities are bad here. We’ve already removed both Monks and Wizards, but both would also fail here. If the psionic classes were not “too many options,” they might have issues with this section simply because knowing how many Power Points to spend (particularly with Augmentation) is very difficult for a new player.
Being able to continue to function despite being out of resources, though, can go a long way towards saving a class here.
Tome of Battle initiating classes, particularly Crusader
These classes have small lists of available maneuvers, and best of all, almost zero traps: a new player can just pick what sounds cool, and it will be. This is almost unique in 3.5. Rather than comments that have been made about requiring too much system mastery, initiators require very little system mastery. They require that you learn their own subsystem (which is nice and simple), but unlike many other classes, you don’t have to learn much about the rest of the system as a whole. Feat choices are less crucial, because you have maneuvers. Magic items dependency is less dire. The classes just function rather well straight out of the box, so to speak.
Initiators involve some resource management, but it’s inherently forgiving: everything is per-encounter, and you can get your spent abilities back through recovery. This is good, because resource management is important, but initiators keep it simple.
I like Crusader best of all here. Not only does he have all the benefits of Tome of Battle classes in general, he also has the benefit of limiting the player’s round-to-round choices as well: only a few of his maneuvers are Granted at any time. His recovery method is automatic, too, which is great. Just print out a deck of cards (Wizards actually offers their own set, which is pretty good), and the Crusader works by drawing several cards at the beginning of the fight, drawing after each turn, and then reshuffling and redrawing if the deck runs out.
The maneuver cards are very useful regardless of which class is used, for that matter. They give the player tangible and easy-to-remember markers of their available options, they can be flipped over to show they’ve been used, etc.
Of the remaining two classes, I prefer Warblade over Swordsage for new players. This is simply because the Swordsage’s recovery method is much less forgiving than the other two.
The Warlock (Complete Arcane) and Dragonfire Adept (Dragon Magic) are solid, simple classes. They get a few invocations, which they can use at-will: doesn’t get any simpler than that. The Dragonfire Adept strikes me as the better of the two: it focuses on Constitution, which is good because it encourages the player to avoid being squishy, and the breath weapon is a bit better than eldritch blast.
Beguiler from Player’s Handbook II
The Beguiler is a really great class: the spells are mostly pre-chosen, but it’s a solid list, and you can use them spontaneously, which is nice and simple. The problem with them, of course, is that they are per-day limited, but the Beguiler has pretty solid skills to use when out of spells, and their number of spells per day tends to be fairly large.
The Dread Necromancer (Heroes of Horror) is also good, but minion-mastery, particularly managing an undead army, is probably too much of a headache – for player and DM. The Warmage (Complete Arcane) tends to be weak, and Warmage’s Edge is a trap, so I don’t recommend that either.
Half-casters (that are actually good)
I don’t recommend Ranger or Paladin; they are quite weak and aren’t really good at very much unless you really dig for the best ACFs and spells for them. Not what a new player wants to do.
But Bard, Duskblade, or Psychic Warrior have merit. These are all classes that do have some problems with the above factors I recommended removing: they have per-day limitations, the Psychic Warrior has Fighter Bonus Feats, and so on. But, they go a long way to remedy these situations by being good at a wide array of things and not being too useless once they are out of spells.
Tome of Magic’s Binder
This class can be difficult to get a handle on because of the poor layout of the book: it’s difficult to see all of your options at once and what they are. But particularly at low levels, the Binder is a pretty simple class, and particularly awesome and fun to roleplay. For a new player, I’d probably try to print out each Vestige separately, and only give them the Vestiges that they currently have access to. At levels less than 7, they simply pick one of those and go to town.