360 vs 383

Depends on what the car is set up for currently. If you have to go changing k-frame, trans/bellhousing, driveshaft, exhaust, etc., then your budget is out the window. Build whatever the car is set up for.
Bingo! As an aside, the machine shop I use now wants an enormous price for a full rebuild. They told me it will now take 4 months and $3500 labor + I supply parts. That puts me into the crate engine cost territory. Just taking a block and heads to them to see what is needed would sting the budget before the project ever got off the ground.