Before taking it to a shop ask around and find a shop that understands the old cars and has a good reputation.

Also, a compression check is very easy to do yourself. Remove all sparks plugs, wire carb all the way open, screw gage in spark plug whole, crank starter a few revolutions, look a gage. Write it down for each cylinder and post up the numbers. No need to pay to have that done. Its very easy to do.