I'm a full timer here, have been for 6 years or so. I don't cross much but talk to lots of people that do.
I think if the registration and title are in your names you should not have a problem with the vehicle. Be sure to get you Mexican Vehicle insurance from Rosie at Pro Alliance insurance here in Penasco. She is a great asset to visitors. You can get it onlline.
You should stop on the Mexican side at the border and get an FMT, Mexican Tourist Visa. Easy and simple, need a passport, cost a few bucks, you pay at the bank across the street. Just pull over to the right after you pass inspection and go into the building that would be on your right as you cross, immediately adjacent to the inspection area. Just go in, fill out the paperwork, open all hours that the border is open, no problems.
Lukeville has been a very safe crossing. Very few problems reported. Traffic can be a little busy but the signage is good to Penasco as you pass through Sonoita. Seems there is more hassle on the US side than on the Mexican side with inspections and slight delays so don't be too surprised. Please also be aware the both Ajo Arizona USA and Sonoyta, Sonora, Mx. are speed traps. Watch the signs carefully and obey carefully. The Sheriff's in Ajo may get right up on your bumper even though you are not speeding. Patience is the key. I will pull over and let them pass if they do that. The Mexican side is in KMPH and is set very slow. Locals will be passing you and riding close but ignore that and stick to the limit. Here it is not the patrol vehicles but radar. There is typically a radar guy operating as you exit Sonoita so watch for that.
The highway between Sonoita and Penasco is better than the highway down from Ajo. Here people tend to fly so don't be surprise to get passed a lot. Mostly AZ plated vehicles in my experience. Little to no speed enforcement here.
As you approach Penasco ther most likely will be a military stop. They have been very polite and are just doing their job of inspecting vehicles both ways.
The winters here are cool, but mild compared to the North Country. Lots of sunny days, maybe a little breezy from time to time and perhaps a shower or two as December is the rainy month here. All in all be prepared to relax and enjoy Penasco. You can find a wealth of information here on this forum and a large number of people willing to answer dumb questions too.