I believe I'd choose to go NM 12 to US 180 to I-10 at Deming.
A few years ago we drove NM 12 & it was a good road at that time. Not that twisting from what I remember.
It seems to a little closer that route: 313 miles compared to 328 miles via US-60 W and AZ-77 S.
It's fairly scenic as well along NM 12 & much of US 180.
South of Silver City is
City of Rocks State Park, a neat place to see & would make a nice overnight stop.
What ever you choose, check the weather before driving to see how the road are at that time. Could be the Wind and/or Snow in the higher elevations at that time of the year.
