So your main problem is having trouble once you're knocked down - that generally means that you're being too predictable with how you get up. Backrolling is probably the riskiest strategy overall, though - many characters have moves that can screw backrolls over big time.
In general, try and mix it up between standing up to guard straight away, and side rolling to avoid more linear attacks then getting up safely during their cooldown. There are exceptions, of course. If you're facing a Natsu, it's almost always best to just sit there and take chip damage from the bomb (after which point you can easily get away safely), because if you get up it's too late to do anything and she can combo into her air-grab.
Anything else you struggle with in particular?