The great thing is that you have a ton of options, even if you're on a budget.
If you're drawn to the deadball era, you can chase the T207 set without needing to get TOO many big name HOFers, but there are still about 50 challenging cards, including 2 or 3 really tough ones.
You could also do Mecca Double Folders or Hassan Triple Folders, which are two great sets that IMO are undervalued and have a good mix of HOFers. Both sets are gorgeous and pretty readily available (particularly the triple folders).
If you're more into the 1930s, the 1934 Goudey set is a nice one. I'm also partial to the Diamond Stars - great assortment of players, gorgeous artwork, challenging low number series, no Ruth or Gehrig.
The 1930s also had a host of premium issues from National Chicle and Goudey that are inexpensive but have a great assortment of players, and a lot of really nice photography. The wide pen/fine pen issues of 1936 are great and I also really like the R303s (though the premiums aren't as readily available in graded form).
Either way, whatever you choose, the folks here will be able to guide you - there's a ton of knowledge on just about every set.
Best of luck!
-Al
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