I also just purchased a 1979 Gulfstar 37 this past August.
I think this particular model receives an unfair amount of criticism which is based off of earlier, more 'motorsailer'-like Gulfstar models. After reading comments about this boat online, I was hesitant about this model until I saw it in person. When I finally did check the boat out, I was impressed by the quality of the the interior, and the functional layout of the decks and cockpit. Also, the rigging is sized appropriately and the chainplate mounts appear solid for coastal and limited offshore cruising.
While I do not think this boat would make the ideal boat for a circumnavigation, I would have no qualms sailing this boat to the Caribbean. The previous owners sailed this Gulfstar 37 several times from Maine to Belize, and did several offshore runs to and from Bermuda. They had owned several large sailboats before this Gulfstar, including a 60' wooden ketch and a Catalina 40 and considered this boat their best yet.
My greatest concern with the boat is the water and fuel tanks that are glassed into the floor. Their location makes them near impossible to inspect, and I've wondered exactly what kind of lifespan I should expect out of a fiberglass tank. When it does come time to install a new tank, I've thought about swapping the location of the battery bank with the fuel tank to ease access to both.
Also, engine access is not spectacular. It's a good thing I am still young because getting around the engine requires a fair amount flexibility and dexterity.
So that's my 2 cents. I'm sure I'll have a great many more comments about this boat after I pick apart every system on it over this winter.