You're gonna spend more than that on the swap, add about 1500 to 2K to that and you're set. Come on, that's only a few more hours of work lol. jk

The 5.3 would def. keep you under budget, but the trans, wiring, and fabricating may push you over 3K.
I just tuned this guys 5.3L that went in a 95 4x4 chevy, and that's all he wanted, something to get around and a nice replacement to his older TBI 5.7. There's nothing wrong with the 5.3L, but if you're looking for power, get the 6L or LS1

good luck