As rivercOIL said, alpine skis will be fine - especially in the East. If you plan to spend more time in Utah, you'll want to try some fat skis - they way smooth out the ride. I bought a pair of G3 backcountry skis last year mounted with Fritschis. In the backcountry they kicked butt. On piste though you do give up something compared with regular alpine skis - not a problem since backcountry, except for the last run home maybe, is an all day experience (which, by the way, makes the AT bindings worthwhile).
Most of the guides we've skied with are on roughly 85mm (underfoot) skis - skinnier than the fat skis you'll see many other backcountry types on.
Guiding, if you can get a couple of people together, will typically cost $140-$150 a day. If you figure a lift ticket would cost you $60, you're in for about $100 extra. It's worth it - no lines, just a few fellow backcountriers, safety, safety equipment, and an incredible day. A good - and less expensive - beginning in Utah is the Inter-Mountain tour between Snowbird and Park City (various stops, not all areas visited). This is a guided group, no AT gear necessary (though I'd rent some fat skis) - and you can hook up with other folks interested in hiring a guide (you may be able to get one of this group's guides). Exum provides top-of-the-line guides: http://www.exum.ofutah.com/Pages/homepage.htm
(We've used Brian Brechwald and Anna Keeling on separate occasions - both were outstanding - and Tyson Bradley has literally written the book on backcountry skiing Utah.)
As for equipment, the Backcountry store is good (http://www.backcountry.com/)
, and so is Black Diamond in Salt Lake City, UT - they can hook you up with some of the most qualified guides in the area. Personally, I've liked working with the folks at Bent Gate Sports in Golden, Colorado (http://www.bentgate.com/)
. I started using them by phone, and last year got to visit the shop. A great place and the people will take pains to make sure you're getting what you really need. There's a place on the Mountain Road in Stowe that carries backcountry ski gear - AJ's maybe? There are a few shops in the East, but the market here isn't very rich for backcountry stuff, so I've always found a better selection out West.
I bought some AT boots... They're useful, but unless you're really going to spend a lot of time at this, I'd skip them... Depending on your feet, they may require more fitting than regular alpine boots - they may have a sloppy fit without it. There are a fair number of good boot fitters around, though far fewer really excellent ones... Jeff Bergeron, who runs a boot-fitting thread here is truly incredible (he fit my backcountry boots) - if happen to be in the Denver area, look him up in Breckenridge (need an appointment well in advance usually). Greg Hoffmann at Stratton Mountain in VT is another excellent fitter. There is another at Killington whose name eludes me...