The LT1 has a number of pitfalls in stock configuration that can add up to a lot of money quickly. The ECU requires a chipped ignition key and must be reflashed to ignore that. If it is a 96 or newer, you need to run a post cat O2 sensor as well as a pre cat o2 sensor. The Opti-Spark is failure prone and expensive. The catalytic converters are bolted to the exhaust manifolds and have a unique output flange stock. Now, you can avoid some of this if you run a stand alone ECU or all of it if you run an HEI and a carburetor. Run a used carb and a junkyard distributor on a GM conversion intake and you have all of it handled except for the accesory drives, which hit the frame (or come damn close!) with anything but the Corvette accessories. I am by no means an expert on this, and have not actually done it myself. This is all based on what I have read over the years. I believe it is a sound hypothesis, but it is up to you what you want to do.
For my $1,000, I would consider finding a good used 96+ light truck L35 Vortec 350. You get good heads, roller cam, somewhat decent compression and upgradability. All you need for that conversion is the intake manifold and a roller cam distributor gear. You can always upgrade the cam and valve springs in the future to make some decent power. Also, the Vortec heads are basically a Gen I version of the Iron LT1 heads used on the B bodies. They are well known for their flow numbers and efficiency.