I'm going to be using number notations. If you're unfamiliar with what those are, look at the top of
this page really quick.
Well, first of all, if you play a character with lead-ins, things can be simpler (like Striker was getting at). For example, Hayabusa (DOA5) has these options after his standard PP:
PPP (same as 6P)
PP6P (same as 6P+K)
PP4P (same as 4P)
PPK (same as H+K)
PP2K (same as 1K)
So really, if you get used to these and their options, it'll all meld together. Look at the standalone versions for each:
6P goes into 6PP, 6PK or 6PK4 (ongyoin stance transition)
6P+K can go into 6P+K4 (ongyoin stance transition)
4P goes into 4PP, 4P6P, 4P2P or 4PK
H+K goes into H+KKK or H+KKP
1K goes into 1KP or 1K4 (ongyoin stance transition)
So really, all those strings are connected. And once you get used to the standalone versions, the way that they connect to his standard jabs will seem more natural.
Note also that characters have recurring motifs. For example, after Hayabusa does a string that can lead into his ongyoin stance, you usually hold the 4 key to make the optional transition. From there, you look into his stance options for any further mix-ups.
Then again, it also helps that Hayabusa is a pretty telegraphed character in that all of his attacks tend to look drastically different and distinct, so they're easy to memorize/notice and catalog. Maybe I'm biased because I main him, but Kokoro, for instance, I find to have a lot of moves that basically look the same, but are in actuality quite different in function.
In general, I would start with learning a few key moves. For example, know (1) your fastest mid, (2) your "best" low, (3) a good stun attack, (4) a basic launcher or two and finally, (5) a punish throw and your heaviest damage throw. Once you feel comfortable with those, start branching out and seeing what other moves might be useful and that you can add into your arsenal.