That budget can get you into some much nicer older cars. For exapmle, around here the C3 Corvette (68 to 82) is a hot entry collector market. You can get into a nice one for $15k or less and get a taste of the culture to see if it's for you.
If I were looking to jump into that hobby I would stay away from new or late model cars. Much less collectible and much more expensive. I would also stay away from project cars (to start with) because of the time and expense required to get them on the road.
Good luck deciding, have fun looking!