The exact break down of Perform subskills is largely up to the table. Most players just pick one Perform skill and stick with it, because that saves skill points; the different subskills are just so you can pick exactly what you are doing. Some players pick more than one for a few reasons, which I’ll get to, but the short answer is, “the rules pretty much assume you’re only using one Perform subskill at a time, because the rules don’t really care that much about Perform.”
Perform isn’t actually that important
The uses of the skill are for making money and earning a name for yourself performing. However, most D&D characters are adventurers, who will have little opportunity to use Perform in such a fashion, and regardless, adventuring pays far better and is much more likely to result in power and influence (assuming you don’t die, of course).
Furthermore, bards don’t actually need to do well on their Perform checks to use Bardic Music. They need a minimum number of ranks (more on that in a bit), but once they have those it doesn’t matter how well they do on their actual check. And since Inspire Courage is by-far the most important Bardic Music effect, and only requires 3 ranks, depending on what you do with your career (i.e. maybe you multiclass or take a prestige class and don’t get the higher-level Bardic Music effects), you may not actually need more than that.
Thus, having ranks in Perform is almost more of a “backstory” tax – if you want to claim that you are an excellent performer, you need to spend the skill points backing that up. Since it’s a matter of who you are and what your backstory is like, the choice of Perform skill(s) is very much tied to your character and up to you. As such,
There is no canonical list of Perform subskills
The rules themselves occasionally reference Perform subskills – a magic harp that requires Perform (strings) perhaps, or a prestige class with ranks in Perform (dance) as a prerequisite. They can occasionally get very specific (there’s at least one book that has special rules for Perform (weapon drill), and a certain notorious third-party book includes rules for Perform (sexual act) – no, I am not joking). But for the most part, the rules don’t really care which Perform skill you have, and never lists any kind of canonical set.
Most tables1 are fine with you picking any kind of Perform you want to make up
Since there aren’t any official Perform skills, and it doesn’t really matter, most tables are fine with you defining your Perform skill however you want it, so long as you state what instrument(s) you use to perform it. A masterwork instrument provides a +2 bonus, but since you can only get the bonus once, it’s usually best to stick to a single instrument rather than have something like Perform (one man band) that requires a whole set, but you can if you want (and your table agrees; in my experience it’s not a problem).
A lot of players just pick Perform (sing) or Perform (dance) just so they can never be stripped of their ability to perform by the loss of an instrument (but see summon instrument for an easy fix to that). A masterwork tambourine (or similar) is sometimes used to get a +2 bonus on Perform (dance), and to qualify for the requirement that allies be able to hear your performance for Bardic Music, but talk to your DM about that before using it.
Having multiple Perform subskills is usually seen as a redundancy
Now, redundancy can be a good thing. For example, if you lose your instruments but someone lends you a flute, it would be nice if you have Perform (wind instrument) as well as Perform (strings). Plus, as I mentioned, sometimes magic items want a particular subskill, so if you want to use both a magic flute and a magic drum you need both Perform (wind instrument) and Perform (percussion instrument).
But unfortunately, the rules also see multiple Perform subskills as a redundancy. There are no rules, to my knowledge, for one person using multiple Perform subskills as a part of a single performance, even though that is a really common thing for musicians, e.g. Perform (guitar), Perform (sing), and Perform (dance) for your average frontman.
As a result, there’s not really a lot of reward for having more than one Perform skill unless you think you’re likely to find yourself required to use a particular instrument that isn’t your top choice. Most people pick just one for that reason.1
But if someone did take several Perform skills, personally, I would rule that the lower rolls were Aid Another (...Aid Yourself?) attempts on the highest roll, so you get a +2 bonus for every additional Perform subskill you integrate into the performance and roll at least a 10 on. Alternatively, you could be ruled as making three separate checks at once, thereby potentially multiplying your monetary reward as well as your chances to be noticed by important people. But the rules don’t specify either of these.
Bardic Music requirements
Bards must have at least one skill with the minimum number of ranks listed in Bardic Music effect in order to use it. So yes, you need at least one Perform subskill with 3 ranks in order to use Inspire Courage; having one rank in each of three Perform subskills will not be sufficient.
Note that none of the Bardic Music effects actually involve rolling a Perform check; you probably will for the sake of determining how nice it sounds, but even if you do terribly the magic still works.2 As a result, strange as it may sound, Perform isn’t actually that important to the bard, beyond having the requisite ranks. Using Perform as a skill is very rarely critical; you can earn much more fame and fortune adventuring in most games than you can Performing, and probably will unless the entire table wants to do a theater game (and even then, I’d argue that D&D is very much the wrong system to use for that).
1 In my experience. Most of the games I’ve played in have challenged the PCs quite stringently, and therefore required reasonably careful choices made in allocating character resources, including skill points. Other tables may find it more common to “waste” lots of skill points on “redundant” Perform skill ranks.
2 I once played a game with a Cha 5 orc bard3 who regularly rolled negatives on his Perform checks despite the requisite 3 ranks, thanks to a couple of Perform-weakening flaws; he managed to get like a −4 modifier or something. We had great fun with his singing being terrible and all of our characters trying to get him to stop singing.
3 Yes I did just put a footnote in my footnote, nyah! Anyway, the orc wasn’t actually a “bard” per se, but rather a homebrew class that got Bardic Music like bards do. I mention this because a Cha 5 bard would be a really terrible choice, considering how nice the spellcasting they get is.