Here is a useful link to a road trip planner http://www.myscenicdrives.com/

I think the northern route might be a bit more interesting. Either way, you're on major interstates most of the way so I should think your car will be OK. We actually sent a writer, Lena Katz, on similar trip a few years ago. You can see some of her pictures here: http://www.flickr.com/photos/awaydotcom/sets/72157623006533712/with/4188064996/. Some highlights of places to check out include Sedona, Albuquerque, and Ruidoso (just one stop on New Mexico's Green Chile Cheeseburger Trail!). You might also want to check ahead for area weather conditions, in case there's a lot of snow that might make driving the southern route a better option. Sorry if this answer is getting to you too late.