I love Mel Torme!

As for particular songs, "You'd Better Love Me" is a good song... And he does a great version of "That's All," which is one of my favorite songs ever. "The Nearness of You" is also really good. Well, come to think of it, almost all his songs are good.
If you're going to get a CD, I have a CD of his called "That's All" which has a bunch of good songs on it, 24 tracks total. I also have a 2 disc album called "The Best of the Concord Years" which is also awesome.

My mom has his New York album, I think it's called "Songs About New York," or something like that. That's a good one, too. His version of "New York, New York" (which is on that CD) is really good, although obviously not as good as Sinatra's. But still good.