Just pull the 350 out of a Chevy van or pickup. It's the same engine as is used in a car, but some of them have better bottom ends for better durability. I would look for a 1987 or newer engine as it will either have a roller cam or at least have the bosses cast in for the factory roller cam parts. The heads will be garbage unless it is a RPO L34 "Vortec" 350 from a 1996 or newer model.
BTW, by the time you have the machine work done, balance the rotating assembly, buy the parts, buy a good set of heads, valvetrain, intake, etc. you will not save all that much money over a crate engine. Plus, you have to figure in the cost of things that go wrong or come up unexpectedly during the course of the build. With a crate it comes with some sort of warranty too, so if it blows up an hour after you put it in, you are not out all the money (unless you did something stupid like run it without oil or water). Also, if your block turns out to be garbage after the machine work is done, you will be out the money for the machine work AND the core. This does happen and I have seen it happen. That is why I get my blocks from the machine shop I am dealing with unless it is a rare or odd engine (like an AMC 360). That way, if it is bad, it's not my problem. Plus, the shop won't charge you that much more for a block than one you pull yourself.