The Catalina 22 was also suggested to me, and I took lessons on one. I ended up with Precision 18 (new). Some used ones at:
Precision Sailboats - For Sale
You probably want a swing keel if you are using a trailer often.
Also, look at Rhodes Mariner 19's......
My P-18 draws only 21" with the board up.
Also, you might give some consideration to mooring. Raising a mast and rigging each time you go might take some of the fun out of it.
Another option is to look for certain clubs and orgs nearby - for instance, in Newport RI there is a non-profit sailing center where you can rent J-22's and Rhodes 19's inexpensively. If you are going to sail only a limited number of hours, it may pay to rent.....even at certain commercial places.
Another small trailer boat is the West Wright Potter 19 - more popular on the west coast than here, but some are often listed.
A lot depends on your budget and what happens to be on the market at the exact time you look. You do have to consider the total cost of ownership - and that is where renting can be a great deal.