Here are a few pre and post war sets that are not massively difficult to complete.
1936 Goudey - Lots of nice cards with a few hall of famers. No super expensive cards. 25 cards in total.
1939 Goudey Premiums R303-B - Great set with loads of stars. DiMaggio and Feller may cost you a couple hundred. 24 cards
1954 Topps Scoops - If you only collect the baseball subset it comes down to only 4 cards. This isn't for everybody as its not really considered a complete set.
1953-55 Johnston Cookies - Three different sets. 1953 is the easiest to complete with no superstars and a 25 card checklist. 1954 has 35 cards including a hank aaron rookie that will cost you quite a bit. 1955 also has 35 cards with a more affordable early Aaron card.
Hope this helps,
Owen
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1955 Topps 171/206 
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