If you're going to go V8, then you'd better be decent with fabrication work. Lots of things to make fit that don't want to. Very easy to go over budget. You should probably get any motor built (Or for a Chev V8, you could go with a crate motor, probably the cheapest way to get a known good build) and you'll be looking at spending half or more of your budget on that. (A quick look says that for a GM 350cid, anywhere from $1400-4000, with the low end of that being about equal to a 7M-GE in terms of power.)
So much easier and more predictable (in my mind) to pick up a 7M-GTE, get it built properly, and drop it in. My 7M-GTE rebuild is probably pretty close to the $3k mark (Though I'm doing much of the work myself) with forged pistons, MHG, new oil and water pumps, 550cc injectors and Lexus AFM, ARP studs, new hoses throughout. When I drop this in, I expect to be making good power with no issues.