Should be able to get a quite nice comon Buffalo Nickel, Kennedy Silver Half, or Ben Franklin Half. Careful shopping maybe two of the three.
You can get a couple of Proof Roosevelt dimes or Jefferson Nickels in PCGS holders, You could get a Proof Presidential dollar in a PCGS holder. The options are limitless.
You can hit up some of those 5 world coins for $1 bowls that you see all over flea markets and coin shows and start your collection off with 50 coins.
If it were me I'd spend that and a little more for a ticket away from California. What your asking is rather difficult due to every area of this country prices are extreamly different. For instance in the Cook County area of Illinois, sales taxes alone are 10.25% on almost everything. So your $10 on something woud still need $1.25 for taxes. Gee I wonder if that is one of the reasons no one is buying cars here. Not sure what it's like where your at but if you have any flea markets, you may find anything from a valuable coin to a AK-47 for that. One coin dealer at a flea market by me has bins full of coins for really cheap prices.
You need to be a bit more specific. There are plenty of "old coins" than can be purchased for $10. What do you like?
A pack of good bullets and that opens a world to anything you want ........................just kidding
That's still pretty inspecific. Do you want stuff from ancient Rome? Do you want medieval Spain? Do you want 19th century American? You can get coins from all of those categories and more for under $10.
For $10 you can start on a nice set of Barber $1/2 in lower grades, say AG or silghtly better. Also, most of the Barber Dimes in G-4 would be nice buys, for much less than $10 each, same for the quarters! PM Me, and lemme know if you want some. Sorry if this in ng.