Probably the cheapest long running set you could complete are Jefferson nickels. Most of the coins you could find through roll searching and even the rarest ones (not counting mint errors) shouldn't cost you more than $20 to obtain.
If money isn't as big of an issue then you have lots of options. I'd suggest getting a RedBook if you haven't already. It is the most respected general price guide for US coins. You should look through it to see what coin styles you like and it will give you an idea of how much it would cost to obtain the coins you want.
Another way to collect might be to obtain a diversity of coins. That's what I did when I started out. I found getting a 2-cent piece, large cent, a Mercury dime, and a Standing Liberty quarter more interesting than getting 4 Mercury dimes from 4 different years.
If money isn't as big of an issue then you have lots of options. I'd suggest getting a RedBook if you haven't already. It is the most respected general price guide for US coins. You should look through it to see what coin styles you like and it will give you an idea of how much it would cost to obtain the coins you want.
Another way to collect might be to obtain a diversity of coins. That's what I did when I started out. I found getting a 2-cent piece, large cent, a Mercury dime, and a Standing Liberty quarter more interesting than getting 4 Mercury dimes from 4 different years.



















