I've just switched to playing on pad from playing SF on stick. I was under the misapprehension that playing on pad wouldn't require execution practice as I've been playing on PS shaped pads since the PS1 came out. I was wrong.
If you've got large thumbs, go into training mode and look at the input display. Pick a combo, enter it slowly (it won't come out, but the sequence will appear on the screen). When you've worked out ways to hit the buttons so that the sequence comes out clean, speed up a little and see if it remains clean. When you're at a speed where the combos are coming out, practice getting them to come out ten times in a row on both sides. When you can do ten, move onto something else. Next day, start your practice session with trying to get ten in a row again. If you can't do it, check the input display and see where you're going wrong.
The goal is muscle memory. Once you've achieved it, you'll free up mental space for making reads and developing strategies. The more repetition you do now, the less you'll be thinking about your button presses mid match, and the more attention you can apply on strategy.
Hope this helps.