think used?
A great source for a decent budget driveline is a ratty/rusty slightly wrecked old car that still runs & drives. There are still a lot out there, at least around here. Sometimes the family will finally part with that old girl that's been sitting alongside the garage for years. Honestly, if you can get the whole car, then you can get it running and maybe drivable enough to see how the engine and transmission is. You may also be able to use the rear end out of the car (or truck) and other goodies too. So for a few hundred bucks, you may have a LOT of parts (even electrical, steering column, brake parts, etc) that you can repurpose for your rat rod.
That being said, don't limit yourself to Chevy donors, or even GM ones. Check your local papers, auto trader, craigslist, etc. and let us know what you come up with! On a budget, as long as you start with a solid drivetrain, you are bucks up, Chevy or not!
One more thing - if this rod is only going to be driven occasionally, why does the engine need to be rebuilt or a new crate motor? My most reliable car right now is an unrestored original '79 Buick Skyhawk. Except for using a fair bit of motor oil, I've driven it from Maryland to Myrtle Beach, SC with no problems at all.
440shorty