You'll have to try some on to see what fits your foot best. Since you're going in October, I would suggest a real boot. Not the trail running shoes that are so popular in Sept. I also prefer uninstalled.
Whites Outdoorsman boot - uninsulated - get the Montana Claw lug sole if that is still available. Best I've used in all types of terrain and conditions. They will make the boot to fit your feet too if you want to go that route.
Try on what ever you have in your area. If you need to order boots online, do it, can always send them back. I prefer uninsulated during that time of year. I wear Crispi because they fit my feet the best of what I have had over the years.
I prefer mid weight and height hikers. Taller boots similar to Crsipi Idahos or Lowa Tibets are a chunk heavier weight and stiffer. Taller and stiffer boots are nearly impossible to stalk quietly. The name of the game in NM or elsewhere with elk is covering gobs and gobs of country. You may also sweat a little more in taller boots? To me weight and comfort are on top of my list. I often use taller boots when there is lots of snow.
Boot brands I've had the most success with are Scarpas, Lowas, and Crispis. Scarpas are great but tend to run narrow. I've had great results with several Lowas over the years (Vantage and Caminos). It's tough to beat Crisipis. I recently bought Wyo's and Dakotas. Crispi recently reduced updated versions of several of their models that you can get for around $100 off....which is tough to beat!
I would highly recommend all leather with the fewest seams available. The more seams the fewer miles you will get out of them. Most synthetic boots have lots of seams and may breath better but likely won't last as long.
It’s very steep where I’m at, and we do lots of packing game out of steep logging units. My custom built Wesco 8” loggers boots work great. If I were going to be hunting on flatter ground I’d probably be on the market for something with less of a heel and a more flexible sole.
I used to swear by Lowa but have switched to Hanwag and prefer them. Lowa still make great boots but the Hanwags I have fit me better. It is all about what works for your feet. I have set of Gore-Tex lined Hanwags for constant wet weather but my other Hanwags are leather lined boots that seem to mold to my feet better than any Gore-Tex boots ever did. You can still waterproof the leather so unless you are planning for nothing but rain/snow I think the comfort and breathability of leather lined boots outweighs Gore-tex in 90% of my hiking and hunting scenarios.
I always start with the soles of the boots before I try a pair on. For the most part, if they don't say Vibram or are of similar quality, I move on. I hate injected molded soles that you find on a lot of boots and would not buy them. That should narrow the boot brands down to quality companies and then figure out what fits your foot. I use a few different brands of boots but my primary elk hunting boots are Lowa and Zamberlain.
What part of New Mexico and is it public land or private? When I hunted near Chama on private lands, I managed with a pair of Danners. If I were hunting public lands in the Carson National forest, I would rather have a better hiking boot such as Salomon, Lowa, Crispin, etc