The question is, what is the "best" conversion gun for this compressor?
In addition of giving good finish, it should be ergonomic to use and easy
to clean.

It's hard to say what is best. A lot depends on the types of finishes you
want to spray and the size of the items you'll be spraying, as well as the
amount of spraying you'll be doing (with choices between gravity feed,
pressure feed, and siphon feed types). I'd suggest having a look at
www.homesteadfinishing.com for some good info and call them or email if you
have specific questions.

A side question is, where the compressor should go? In the finishing room
with the spray gun, in the main workshop area for easy access, or outside
to reduce the noise?

You'll want the compressor outside of the spray room and indoors. You could
get air lines piped in and will need appropriate filtration and moisture
traps.