The longer I look for the boat the more I realize that it all boils down to a series of compromises.
Need a boat that I can single hand if necessary,
I am leaning towards a centerboard or, if fixed, a maximum of 4'6" draft. Neither of us like the look and feel of the newer boats - Hunter, Ben's, Catalina's, etc. Each time I look around I keep coming back to an Island Packet, Tartan 37C or possibly an Allied - all in the 36-39' range.
A used Tartan with a few years on it should be well within or even below your budget. IP's tend to demand more of a premium, but there is no particular rhyme or reason to any of this. The "newer" boats (e.g. Hunter, Benneteau, etc.) might seem less classic, but they still tend to keep the ocean out. They also usually offer huge gains below decks vis-a-vis more "classic" designs.
Find a boat you like the looks of, with a profile you understand and a layout you can live with. Anything under 40 feet with a single mast is a non-issue for single handing (I'm 33' with winches from the early 1960's and no roller furling and I single hand all the time).