Hello and welcome to the sport. Being in the Las Cruces area and detecting for the last several years I may be able to help you. The soil has a high level of minerals so depth is not always there even in the best of conditions. The two entry level machines you mention have the basics and a preset ground balance or ground balance when you turn them on. As you progress with your knowledge and learning of the sport you will want to upgrade your equipment. Even a basic entry level detector will work in these conditions here. But you will find even the most remote areas full of trash or nails that set the detector off with every step. You also need to know the rules of the State and code of ethics as it is important we not leave our sport to being regulated out of existence. You can not detect state parks, or federal protected areas. Even having a detector in some places can get you into hot water. There is also historical areas that should not be detected.
So first, get the best detector you can afford. Expect to pay $700.00 bucks or more but there is many well under that price that will do a great job. Too many brands to list and too many options as you may have already found out reading the forums. A sponsor here on one of the forums will be happy to discuss your needs and get you started. Usually the more you pay for a metal detector the better the options, so look at price. Weight, battery consumption, depth, discrimination, coil selections and so on can be confusing. While buying used can get you a great deal. There is a lot of fakes out there and you may not get a warranty. I suggest buying new and get a warranty.
My last purchase was actually a down grade to a less expensive detector. While my Fisher F75 is more than capable with it many coils and uses. I purchased a Garret AT Pro with a two coil option. I have seen the 5x8 coil used and it performs great on these old sites and trashy areas you are talking about. A large coil covers more ground and depth, but you need the separation of a small coil to cut through the trash. The difference between the two detectors in a nut shell is the AT Pro's Iron Audio feature I fell in love with. It allows me to hear the iron in the ground and check deep targets with a push of a button. Now there is many many other features of both machines I wont go into here but used that as a example.
So I suggest you down load a pdf version of the manuals of these two machines or any detector you are looking to purchase and see what the detectors actually do. There is a lot of reading there but you can also watch many of the videos posted on line too. Kellyco also has a compare option buried in there web page that lets you compare two detectors side by side. So research is key in your purchase and your hunts.
As for courtesy and code of conduct. Its common sense. First always have permission. Now asking for permission usually gets you a no. Be creative how you get permission. Know the laws and rules if on BLM land. For instance, you are allowed to meteorite hunt on BLM land. wink wink. I also dont hike with my detector assembled. I have a extra long back pack made just for that reason. You start pulling anything out of the ground and folks will start un inviting you quick. You also have two pockets, one for trash and one for coins. Fill your holes and carry out your trash. Also be ready to be asked a lot of questions if you encounter folks.
One thing you will want to do is share your finds. When posting pictures be sure location is off and you shoot in the raw format. Never tell where you find stuff or be prepared to fill holes and pick up trash next time you go out.
Some items you will want to consider is equipment. A good digger like a lesche, and a pin pointer to help find dirt colored finds easier is a must. You can buy a cheap digger at home depot in the garden department for about $10.00 buck. You can get a cheap pin pointer at Harbor Freight for about $17.00 bucks. You can print a 40% off coupon for Hobby Lobby and get a economy detector for about $60.00 bucks. Or you can get some good equipment that will produce through a sponsor here.
Ok now for the part you dont see in the advertisements or reality shows. Be prepared to dig trash. Your gonna dig a lot of trash. Also you will need to spend time with your detector to get really good with it. Start by placing a dime on the ground and setting your detector up to that. Also there is tips and tricks you can learn to increase your finds.
If you are local to this area know First Texas is just down the road in El Paso and they are a great bunch. I have met a few of them and they really hunt with the machines they make and sell. If you are local let me know and we can get together and Ill be glad to show you the two machines I use and what I mean.