1940 Play Ball might be a great choice for you - the set includes contemporary players such as Foxx, Ott, and Greenberg, but also has a nice selection of recently retired players and old timers. Overall it gives you as close to a full picture of the pre-WW2 era as you can get in one set.
The design is simple and inoffensive to most people, and the backs have an often interesting write-up on the player. Prices are quite reasonable even for Hall of Famers, and you can get mid to low grade commons for a couple bucks each if you buy in groups to start with. The roadblocks will be Joe DiMaggio, Ted Williams, and Joe Jackson, but you could find a decent copy of those for $500 or less if you shop carefully. I would bet you can put the rest of the set together (240 cards) without paying more than $50 for any card.
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