In many cases just going down just a full size is adequate. This does make the shoe a little uncomfortable, but a tight shoe does two good things. One, it gives you better "foot feel," so you can really sense those tiny knobs and ledges. Two, it ensures that the shoe won't rotate on your foot when you really crank on it. If that happened, you'd slip right off whatever edge you're holding. So buy a shoe that's about as tight as you can stand. Super-tight fit is less critical for general mountaineering and when starting out. But serious rock climbers put up with all sorts of pain to squeeze into as tight a pair as possible.
Lots of good choices in shoes out there. You'll want a lace-up shoe; the rock "slippers" you see are for advanced climbers whose foot muscles have built up. I like the Five- Ten Spires ($99) a pretty comfortable shoe for getting the hang of rock. La Sportiva's Enduros ($125) are a classic shoe, good for beginners or intermediates and all-around rock and gym work. The Boreal Equinox ($129) is another shoe that works well for most people of most skill levels on most rock or gym walls. Try several different shoes on, and see what fits best.