It takes a bit to blow your team up. I did it in the middle of last season and it worked out. I sold my guys off and replaced them with significantly better ones. Free Agency was a big component - they were just better than my original team and my early trades.
It depends on how much you can get for your current trainees relative to buying new ones. The draft is random on position - you could easily get 3 centers next season. Your best bet is to pile up cash, then shop for trainees over a couple weeks at the start of the season and try not to overpay. Free Agents are often your best bet as they start at lower prices - just have a target price so you do not go too high on any one guy. Remember you will need at least 4 guys, so try and budget for 4 good ones.
I think the overall size of the market is growing and there is a clear premium for great shooters. It definitely seems that an inside focus is easier to use for winning than outside - so you might have a few struggles on the field until you have a competitive team. The key to BB is to have a good balance.