The Real Book, Volume One (the legal version by Hal Leonard, which is a legalized, corrected version of the old, illegal one) contains more of the tunes that you will typically encounter on a gig. As to why that's so, it's a circular situation: lots of folks have used Volume One on gigs, causing those tunes to become even more more popular, causing folks to get Volume One, causing...you get the idea. By the way, the book I (and most folks) call "Volume One" doesn't usually say "Volume One" on the cover, it just says "The Real Book."
Bass clef might be handy, as Burk48237 mentioned, but if you want bass clef, I'd stick to the bass-clef Hal Leonard version of The Real Book, Volume One for the most standard tune (and key) selection:
http://www.amazon.com/Real-Book-Bass.../dp/0634060767
The Sher "New Real Book" series is very well put together and very accurate, but its tune selection, while excellent (lots of great, underplayed tunes), is not quite as standard for your generic jazz gig. I highly recommend all three volumes (plus the Standards and Latin versions), but I wouldn't start with them.
Of course, eventually, you'll want 'em all. Then again, by the time you become so into jazz that you've acquired them all, you'll probably have played most of the tunes so many times that you'll have them memorized and won't use the books much anymore....
If you have an iPhone, other smartphone or iPad, the most flexible one is the iRealBook:
http://www.irealbook.net/iReal_Book/Home/Home.html
It has no melodies (for copyright and space reasons), but you can transpose any tune to any key instantly, load or notate more songs, and the library is already huge. It costs $7.99. That's about the only real book I occasionally use on gigs anymore. Oh, and its creator, Massimo Biolcati, is a fine bass player!
