Tony, I think Ma's got the right idea. Finding the right key for your voice is important. I have a kind of limited vocal range as well (you ought to hear my yodelling attempts) but I'm able to sing most songs I want to by changing keys and using a capo when needed. Takes a lot of experimentation. Tough to beat mother's advice (also a great tune).
One easy to sing tune that most people know and love to sing is Freight Train but the problem is getting to it before someone else does. Good Luck, Frankie