Older Full Keel boats
There is a lot to this topic. More than I have time for this morning but in a general sense, there were good boats and poorer cruising boats from all eras. Many, if not most, 1960''s era boats are going to be very ''tired'' by now. As boats age, there are a lot of things that happen. Some are reversible and some are not. Obviously,deck hardware, keel bolts, rigging and sails can be replaced, engines rebuilt or replaced, electronics upgraded, and so on. But things like bad hull to deck joints, fatigue at high stress points, delaminated encapsulated keels and those type of basic structural issues are not not so easily dealt with.
If I were in your shoes I would be looking for a boat between 26 and 30 feet, up to about 32 feet max. that someone has lovingly maintained, and upgraded. One thing about older boats is that the cost of ''bringing one back'' far exceeds by several time the value of the boat on the resale market, so if you find one that has been carefully upgraded and maintained, the final cost will usually be less than buying a fix-er-upper.
If I had to suggest just a couple boats from the 1960''s that for the kind of thing you are considering, I would probably suggest a Tartan 27 first and perhaps a Seawind Ketch as a distant second. Almost anything that you bought from this era will need bigger tankage and some careful preparation.