From Eddie Bauer's Essential Hiking Daypack Bottle to REI's Basic First Aid Kit and L. L. Bean's Adventure Medical Ultralight .5 Kit, nearly all the major outdoor retailers offer some form of first aid gear for under $20. The items found in these packages could be the difference between life and death in some cases, and make a fairly painful hike a little more bearable in others.
Although I think the first aid kits compiled by these esteemed veterans of outdoor supplies are beneficial and useful, and serve as wonderful places to begin your safety checks, I would also encourage you to consider compiling your own first aid kits, specifically tailored to New Mexico (or your eventual destination) and your own personal needs (I myself never hike without Benadryl; your first-aid kit might require an epinephrine pen).
To begin: Find some sort of waterproof container. Eddie Bauer, of course, uses a water bottle (although a reviewer of REI's LIfeline First Aid Kit in a Bottle says bottles are difficult to unpack and repack. If you opt for the water bottle, choose one with a wide mouth and make sure your kit is loosely packed); L. L. Bean a silicone nylon bag; REI a sturdy plastic box. For day hikes a plastic box or water bottle should work effectively, though if you're camping or backpacking, you should consider size and flexibility. A nylon or waterproof bag or flexible case will be much easier to pack. For the paranoid, attach a carabiner to the package and hook it to your backpack.
Essentials:
• Bandages. At least a few small or medium adhesive bandages, as well as gauze or an elastic bandage for sprains. Adhesive tape is also useful. One or two packages of antiseptic ointment will also be useful in case of open wounds.
• Aspirin, ibuprofen, Benadryl, epinephrine, antacids, or other drugs you may need. In the Southwest I also suggest a snakebite kit if possible. L.L. Bean also suggests Hydrocortisone cream.
• Scissors (or a pocketknife) and tweezers (included in some pocketknives). I left my tweezers at home on one memorable night hike in Gallup in which I found myself halfway up Pyramid Rock with cactus spikes in my thigh and no tweezers in my pack. Don't make this mistake in New Mexico!
• Moleskin. There are few things more uncomfortable than blisters in new hiking boots when you're halfway up (or down) a mountain.
• Sunscreen and insect repellent. Comfort items, really, but why plan to be uncomfortable?
• A needle, thread, and safety pins. For bandages, for trousers, for shoelaces, for anything and everything.
• Water purification tablets. Water, as I have mentioned before, is one of the most essential items to take on a hike, particularly in the desert. If your water supply is running low and you have (by some miracle!) a chance to refill at a mountain stream, make sure you can also purify the water along the way. Water-borne parasites (giardia) can disturb one's gastrointestinal tract for several months and require extensive and expensive medicines. Spend a little now on iodine tablets . . . save a lot of time, pain, and money later.
• A mirror, flashlight, and whistle. These will each, in certain circumstances, facilitate your journey home after your injury. If you're delayed on the trail, the flashlight will help you make your way home or enable you to signal others in the dark. The mirror and whistle will summon aid.
• Matches. If nothing else, these sterilize instruments you will need to treat wounds. They can also be used to start fires for boiling water (at high altitudes, leave the water boiling one minute for every thousand feet to purify it) and, in cases of extreme necessity, to cauterize wounds.
• I'd also throw in a small but packed energy bar or gel in case your treatment leaves you out in the cool longer than you expect. Nutrients do wonders for boosting adrenaline, which will help keep you warm and alert.