IF you have a big family as you said 14 people, I really recommend that you look for a place with lots of non-ski activities. IF you guys are used to live at sea level, low altitude, humid climate I doubt you guys are gonna be able to do ski the whole day, every day, the whole week. You guys are gonna get very tired just with the 2 hours beginner class, so of the mountain activities should be one of your priorities.
Also remember to keep everyone very hydrated! Avoid soft drinks and get water or sport drinks, gatorade/powerade kinda thing and drink a lot! This is very important on high altitude! When I used to live at sea level, I spent 5 weeks in Colorado Springs, which is about 2k feet lower than Aspen, and I had a hard time adapting to the altitude during my evening runs.
So don't plan to many hours of skiing per day, plan lots of other activities, keep everyone with their bottles of water! Specially for first time skiers, just the mountain environment is awesome, you guys go do a class, ski for a couple of hours then you will go to the lodge and will have a lot of fun I`m sure! The ski area/city/village environment is really fun and I`m sure you guys will enjoy!
So if you pay attention to the details the altitude in Aspen shouldn't be too much of a problem, and it is a nice place. I haven`t been there skiing but the city is awesome and very appealing! Your "base camp" is going to be L.A., so traveling to Aspen is a long shot and you all have to catch a plane, I would discard Park City as well. It`s on top of most recommendation for family trips where just skiing is not what travelers are looking for!