Help a newbie out here...
1. What's the strategy for building a team on such a limited budget?
2. Will the below average AAA players contribute at all or will they mainly just help provide PA and IP fill in?

Figure out your target price range and get the best players in that range. part timers are sometimes better value but harder to manage. 
plan to use all of your AAA hitters.  some are ok and some are weak but if you use them you don't have to pay for as many PA so you can afford better hitters. your AA pitchers won't be much, maybe 50 innings each and they're probably bad. maybe 200 PA per AAA hitter.