For most Corvette owners, the engine is the heart and soul of the car, and a point of intense interest when it's time to freshen up the car. The engine is often the attribute that attracted the builder to that particular Corvette in the first place. Many vintage Corvette enthusiasts will pass over cars with basic engines and select only those with the more powerful big block. But these days, even the base engine cars are rising quickly in value, and really, are you going to drive your expensive and collectible C1 or C2 Corvette to the limit of its performance potential? Probably not.
No matter how shiny and clean the engine in your older Corvette may look from the topside, chances are good that it's probably gunky on the bottom side, and it may have serious problems lurking beneath the valve covers. When you roll out your vintage Corvette, you want it to look and run just as good as it did when it rolled out of Flint, St. Louis, or Bowling Green.
The challenge is that few enthusiast level Corvette owners are qualified to rebuild and restore an engine. The process requires considerable skills generally possessed only by professional engine builders, plus access to a whole bunch of expensive machine tools that typically cost tens of thousands of dollars. If you haven't rebuilt hundreds of engines before, do you really want to learn from mistakes made on your original numbers-matching Corvette engine? I didn't think so.
The question about rebuilding your own engine comes back to your personal goals for your Corvette. If you want to learn about your car and do as much of the project by yourself as possible, then do your own engine assembly. If your goal is just to have a nice Corvette to drive or display, then you really should have your engine built by a professional.
Before you even think about performing any major service on your vintage Corvette, go and get yourself a good supply of books - you'll want restoration guides and repair manuals. This is not so you can do the work yourself (though they're absolutely necessary if you decide to go that route), they're so you're educated about what needs to be done.
If you don't already have a good set of books, check my Corvette Library page. All the major works (and many other good general backgrounders) are there.