Well I can't speak to halves or quarters(besides me trying to find all the ATB quarters) but I search mostly cents and nickels. For cents I keep wheats, IH's, proofs, foreigns, and any obvious errors. I also check about 10 different dates for WAM/CAM's and DDO/DDRs. The same goes for nickels except I keep pre-60's(though I'm getting quite a few and may pair it down to a roll per date/mm), wars, buffs, foreign, proofs, etc...
Simple answer, anything worth over face. What's worth over face? you'll find out yourself through research
you could get yourself a couple of whitman coin folders an just start filling them.. cents an nickels are easiest to start, especially if your roll searching,
Everyone tells me im crazy but i collect everything 1979 and older in all denomenations except halves which i only keep rare dates that only have like 12 million mintage. i also keep all copper pennies, errors, and world coins. Look for any war date nickels and any silver (64 and below in dimes through halves) ask your bank if they have big dollar coins sometimes old people bring them in! Collect what you want its a fun hobby!
