I think it's generally a good idea for someone just beginning to experiment with traditional bows to start out with a recurve. Keep the longbow option open though, because if you get the bug, you'll eventually have one anyway.

Define 'cheap'. Are you looking to pick up an old used bow around a hundred bucks or could you spend upwards of $250 - 300? If you want something inexpensive and don't mind doing some gambling, then you can get a vintage Pearson or Shakespeare with a lot of shooting left in 'em for $100 or less. Sometimes a lot less. If you want a new bow with a warranty, then I'd recommend the ChekMate Falcon.

www.recurves.com

Or you can look at some of the Samick/Aim/Internature bows.

I highly recommend picking up a copy of "Become the Arrow" by Byron Ferguson. I like his method of aiming. I like some of the recurve-specific information in Asbell's "Instinctive Shooting", but ignore much of what he says about aiming.