I went through a similar process when I was buying my boat. The problem will be finding a racer in your price range that has a suitably robust rig for the rigors of continuous offshore work or which is shoal enough for island hopping.
In a general sense, I would look for early IMS type racer/cruisers, or some of the one design keel boats which were not designed to any specific rule. When I was doing my search some of the boats that I considered were the Frers 36, Tartan built Soverel 39 (negatives IOR and fragile rig) , Farr 37 and Farr 38 (Design 72 and not the earlier IOR design, AKA Farr 11.6), J-36, J-35, J34c, J-39, Express 37, Oyster Lightwave 39 (my favorite).
There are a number of older Ostar, and Open class boats out there which can sometimes be purchased cheaply. You probably can find old Open Class 40's and 50's in your price range. They tend to have deep draft and minimal headroom, but they were designed to go offshore, single-handed and very fast. Here is an example of an old Open class 50 that has been nicely modernized.
Photos of Open 50 Jules' Jewel
The other way to go is to look for old performance cruisers. The Australians, New Zealanders and South Africans latched onto non-rule related sooner than the rest of the world and produced some neat performance cruisers back in the 1980's. For example, a couple of these that you sometimes see cheaply are the Farr 1220, and Farr 44.
If you are not planning to actually spend a lot of time offshore but want a good sailing boat capable of occasional offshore passages, I think that the Beneteau First 42s7 is a very nice design. I would think the Beneteau First 38 or First 38s5 would also fall in this category.