SO happy to share inspiration @indigocean. Let me begin by sayin I'm not very familiar with propagating prunus (plum genus) via cuttings (as in NEVER done it!). Typically this genus is seed grown and grafted with a known cultivar. That said if you can get a root sucker (an upward growing shoot near the base) and keep it moist (perhaps wrapped in wet newspaper or coir or potting soil) it may root. Some crushed aspirin, willow tea or rooting hormone may encourage root development.
As for the right environment, plums are generally hardy, although some more than others. Ideally you could find a wild plum and graft the California plum onto it. Chokecherries grown over a large part of NM, so if you could secure a seedling tree this may make a good candidate. Eucalyptus are notorious for quick growth and for being "invasive" meaning they take over native habitat, but I wouldn't be worried about introducing a "non native" plum to NM, but it's always great to be mindful of such things.
Thanks so much!
My grandparents lived in New Mexico, and that is where I spent my summers as a kid, so what I can say is, it depends upon exactly where you are.
As long as you nurture the cuttings for the first year or two, you should be fine, and they will probably do well over time.
If you are in extreme northern New Mexico, as in Zone 2 near the Colorado border, then you may want to nurture them longer, and give them a high tunnel or greenhouse, in which they can thrive without having the extremes in temperature and high winds that that area is known for.
In the end, it is your choice, and I wish you well in any case.
Regarding eucalyptus, as a native Californian, I totally get where you are coming from. They are amazing, and often beneficial trees.
But, as a fourth-generation conservationist, I would never knowingly propagate eucalyptus on the West Coast of the U.S. Or, really, anywhere in the U.S.
The fact that a plant or tree has beneficial qualities does not automatically make it a great idea for wherever it happens to be growing, as it may well be outcompeting native species that are even more beneficial for their current locale.
Every space needs to be considered on its own merit, and each species being considered for said space needs to be considered accordingly.
For the record, my husband and I own a small building lot in northern New Mexico, which we purchased because of my great love for the area, and my memories of great vacations taken nearby with my grandparents when we were kids. I'll be happy to share what I know.
Good luck.