Stamina doesn't take too long to train, as long as you don't have trainees. I'd just finished a cycle of training and so was able to push stamina up between seasons, and on and off ever since.
Another thing people often look at is how high a few of their players are in a particular stat. I prefer to look at it from the bottom end. You want to avoid having especially low PA for example on any player. Avoid weaknesses and you can get away with your best player not having huge PA.
My promotion last season actually came with players with less OD on my three outside starters and less PA at the high end than I'd have in my previous promotion season. To avoid TOs HA is possibly as important (or more) as PA.