Thinking in fighting games...
It sounds to me like you are WAY overthinking it man.
Now I'm not saying that one doesn't need to think during fighting games, but in general what most people (ok, me anyways. But I assume for others...) are thinking about are meta-level concerns like "Man! Does this guy EVER use his low string?" or whatever. For the rest of the stuff "we" just "zen it in".
If you're having problems with combos though, I find one thing that can really help is to get your launcher~first linker down on lock in practice mode. (Might take 2 minutes, might take 2 hours, just depends on you) then (still in practice mode) set the opponent to AI->Expert.
Now your goal here isn't to rushdown and destroy the AI. It's garbage and pretty exploitable and you're not gonna learn anything useful from it. What you want to do here is basically evade whatever the AI throws at you til you find something he does to be punishable, at which point you want to use your newfound string (which you now have on lock) to punish it.
Now IN THEORY this should be just as easy as it was when the dude was standing still, but most people find that in reality that's not quite how it works. Things change when the bricks start to hit back as it were.
Anyways, once you get the string to a point where it's not just "on lock", but it's near 100% when used as a punish, set the AI back off and try adding the second link to the string. Here's the cool part: It will likely seem REALLY EASY to you now to add the second link where previously it seemed impossible! That's, of course, because the problem you had probably wasn't really the link at all, it was probably just trying to commit too much at once to muscle memory and inadvertantly creating a habit of making bad presses.
Just a suggestion,
tehm