Basically, three are three "must have" filters for landscape photography. For someone just getting started, preferably in this order: Circular polarizer (CPL), Graduated Neutral Density (GND), and Neutral Density (ND). Some may argue that GND's aren't really necessary since you can take multiple exposures and blend afterwards, but my preference is to get it right in the camera to minimize the PP time later.
CPL: nice sky effects, reduces/minimizes/enhances glare on reflective surfaces such as water, foliage etc, enhances saturation, plus others. Can also act as a 2-stop ND filter, depending on how much you dial in.
GND: used to balance the exposure between differently lit portions of a scene. Its strongly recommended that you stay away from the round GND filters and stick with the rectangular type.
ND: used to reduce shutter speed in brightly lit situations by cutting the amount of light reaching the sensor (silky water effects, smooth out water, etc). Other uses as well, but this is the typical use by landscape shooters. Just the opposite of the GND: these, you're better off with round filters as opposed to square or rectangular. If you stack square ND filters in a holder, there are too many areas for light to get between the filters and cause exposure problems. Go for round ND's.
For GND's, most people start with a 2-stop soft and a 3-stop hard filter. You can add to them with a 2-stop hard and a 3-stop soft if you wish. I'd recommend Hitech filters as a good, middle-of-the-road filter. I've been using Hitech for years without any problems. Also, I'd go with the Lee filter holder as opposed to a Cokin P wide angle or the Cokin Z-Pro...its just a much better design. In the southwest, you will come across the need to stack GND filters...the Cokin P only has a single slot and just won't cut it for stacking.
For ND's, I carry a 3-stop and a 6-stop. Since a good CPL can do double duty as a 1 or 2-stop ND, no need to buy these. If I need somewhere between 3 and 6 stops of reduction, I can use the 3-stop and stack the CPL for additional stops. More than 5, I then have the 6-stop. With these two filters, and the CPL, I can get anywhere from 1-11 stops of reduction. Of course, depending on your focal length, some vignetting can occur when stacking these filters...but I'd rather get the great shot first and crop later than not get it at all.
For the round ND's and the CPL, my filter of choice is B+W, but Hoya is a good brand as well. You can get excellent prices on B+W and Hoya filters here:
Just be aware that they're located in Hong Kong, so shipping may take longer than normal. You'll need to allow for that if you order from them.
For GND filters and holders, here's another link to a very reputable dealer:
Reverse GND's carry a pretty hefty price. Basically, a reverse GND is dark at the center of the filter and fades out as it reaches the top of the filter, where a typical GND is darker at the top and fades towards the center. If you have the money to spend on it, that's up to you. But for the price of a single reverse GND, you can probably pick up three standard Hitech GND filters. These alone will take a bit of practice to get used to...the reverse just adds another thing on top of all that.
Sounds like a great trip...good luck.