I will assume we are converting to a GM V6 Engine.
The lowest cost route is a 2.8-3-4, cast-iron head RWD engine. This will be a budget conversion, with materials coming in under $1000. I don't feel that it makes sense to pay a restoration shop for this kind of work, though there are many successful conversions out there that have been done by owners in their spare time. I can help supply the parts needed, if you want to build one of these.
One can also use the RWD engines with the high-end components from British Car Conversions, though the savings from using a RWD engine are small when added to the entire package.
I would choose a 3.1-3.9, aluminum-head FWD engine, converted to RWD with a MARC kit from BCC.
The 3.1 and 3.4 liter versions are finally showing up in West Coast wrecking yards in useful numbers. Used engines can be had for as little as $75, up to virtually new low-mileage ones for several hundred.
Since they are such new engines, the 3.5 and 3.9 liter units cost closer to the $1000 mark, depending upon the mileage. Additional work will be required to separate these newer engines from their factory brains, since the variable valve timing cannot be controlled with current aftermarket ECUs.