Buying my first ski - don't even know where to start!

Skis are way overrated.  Seriously, the most important thing you will ever buy for skiing is boots.  Go to the "Ask the Boot Guys" forum and read the wikis about fitting and terminology.   Assuming you already have boots, if the place where you got them didn't do a shell fit they are either too long, too wide and mostly like both.  Boots are what control your skis so if you have a boot that is too big, every time you try to turn your foot first has to move inside your boot before the boot can "tell" the ski what to do.  If you were skiing trees that time can make the difference between going around a tree and colliding with it.  The most important thing any beginner/intermediate skier can do to improve their skiing is getting properly fitted boots, from a competent and experienced boot fitter.  As long as I have my boots I can ski on just about any ski in any conditions and have a pretty good time.  If I had a pair of my old boots from 7-8 years ago it won't matter what ski I'm on, I'm going to have trouble controlling it.  You're going to be in Utah and there are several competent boot fitters in the SLC area.  Brent Amsbury in Park City takes care of mine and there are others.  The advantage of getting the boots there is that if they need some additional work after the first day on them it's fairly easy to get that done, not so easy if you're several hundred miles from the person who fitted them.

Have fun in Utah.  Buy properly fitted boots and demo some skis with an 80-90mm waist, camber and early rise.  A ski like that can be used just about anywhere as long it has good edge hold for eastern conditions.

Sounds like you want a versatile carver to me- 70 mm or so underfoot and 170 cm or so in length.

As your skills improve, you may find you want to get something that makes it easier to handle off piste, but for now something along the lines of the Dynastar Contact 10/11/Ltd that I use as my on piste/hard snow ski.

I think this is similar, but a touch stiffer (which could make it a bit too much for you until your skills improve) http://www.ebay.com/itm/Dynastar-Contact-Cross-Fluid-172cm-2011-Skis-w-PX12-Ti-/310375159797?pt=Skiing&hash=item4843cd17f5#ht_3286wt_1031

Haven't skied this, but it is for sale here and might work

http://www.epicski.com/t/108779/for-sale-blizzard-supersonic

Lots of other possibilities in this class

I recommend a cambered ski between 70 and 80mm at the waist.  Rocker is all the rage now, but if you're not skiing pow I really feel you can get better energy and maneuverability from a purely cambered ski.  Why compromise?

LOTS of great carving skis out there, but you may have to hunt them down--carving is not "popular" these days... Ski shops will try to sell you fat skis and convince you off-piste is the only way to go.  If that's not you, ignore them.

If you have the money, a Kastle MX78 or MX88 is an extremely versatile and powerful ski that literally everyone loves.  For a ski with a tighter turning radius and tons of energy, I recommend a Head Supershape Magnum (72) or Titan (78).  In the carving arena you will have options for a GS type ski (long radius and meant for pure speed), or a SL type ski (super tight radius, fast edge to edge).  Unless you want to break the sound barrier I'd lean toward a tighter radius ski in an appropriate length (about 170 for your height/weight).

There are some good "all-mountain" skis out there too, but realize they are inherently compromises and won't give you the same feel and performance as a dedicated carver, if that's your thing.