Congratulations on your decision to move to one of the best areas ever. I'm a Denver metro area native and EMS student, essentially an EMT-B (just need to take the written and shuffle the paperwork). I also have an extremely accident prone family so I'm somewhat familiar with the ambulance companies around here.

Here's what I know about ambulance companies in the Denver area based on experience and what I've heard from others in the field:
I would advise against working for AMR in the Denver area. They have a lackluster reputation, are dealing with a bunch of issues right now (a "paramedic" of theirs was recently discovered to be just an EMT-B ) and they do not do any 911 in the Denver area (they do 911 in Colorado Springs, however, but that's pretty far away).
From what I have heard, Rural/Metro is a good company to work for. They work 911 response in Aurora, which is very close to Denver through a partnership with the fire department. Other than that I don't know too much about them.
Pridemark is another private company that operates in the North Denver Metro area as well as Boulder. They are the exclusive 911 EMS provider in Arvada and Wheat Ridge, which are large cities just outside Denver. I rode on one of their ALS rigs for my EMT class, and I was pretty impressed by the people I met. It's a small company so it seems like they have a pretty tight community. Everyone I met was extremely friendly and eager to help me, even the dispatchers. A few years ago I was transported by them from one hospital to another and was also very impressed by them as a patient. They have wheelchair vans, BLS rigs that do interfacility transport, and ALS rigs that do 911 and interfacility with a medic/EMT team.
Pridemark website.
Action Care operates in the South Denver Metro area, especially in Littleton. They contract with Littleton Fire Rescue and Sheridan Fire Department (an extremely small dept) and pick up some of their 911 response. I'm not sure what their relationship with SFD is, but I know that LFR basically hands over many of their "BS calls" to Action Care. I rode with an Action Care ALS rig for a ride along and feel pretty neutral about the company. For the first hour or two we were a BLS rig because the paramedic wasn't there yet (long story), and to be honest one of the EMTs, who was new-ish, struck me as a complete idiot. I would not trust him at all. Thankfully, he left once the paramedic showed up and the other more competent EMT-B stayed. The rest of the shift went well but I was not particularly impressed by them. Just my personal opinion though. They have wheelchair vans, BLS rigs that do interfacility transport, and ALS rigs that do 911 and interfacility with a medic/EMT team.
Action Care website.
Denver Health Paramedic Division is the exclusive EMS provider in the actual city of Denver. They are a hospital-based service. Despite some recent negative media coverage concerning their response times, they have a very good reputation. The pay is good and they have a much better benefits package than any of the private ambulance companies. They work much more 911 than the private ambulances because many area fire departments have a very strong EMS division and the capability to transport... except for Denver Fire, which provides no transport and very very very little EMS. So DHPD doesn't have any competition from fire for 911 EMS. I don't believe they do any interfacility transfers except for their CCT rig.They have ALS rigs with medic/medic crews, BLS rigs with EMT-B/EMT-B crews that work 911, a CCT with an RN, and drunk-vans that take "public inebriates" to detox. Since a lot of people want to work for them and they have their pick of the litter, you will need a good amount of experience to be hired. Also, I doubt they will have any openings for a while around the time you're moving here because they're hiring on a whole crap load of people for the DNC that they may or may not need afterwards.
Denver Health Paramedic Division website.
So yes... sorry this was long-winded but I hope it helps. Let me know if you have any questions or need help with your move.