Hey Nick - yea the dog thing is tough and seems hit or miss. I'm more than willing to chat about this more with you if you are interested in pursuing it further. I also now have two rafts and a perfect first trip just to get your oars in the water would be the upper section of the San Juan River. Could do an easy one or two nights. Perfect river to try things out and get a feel for it.
Raft choice comes down to a lot of factors, size, material, type of trips, etc. Every type of raft material has pros and cons, I grew up rowing hypalon boats (like NRS and Avon) and loved them for their ease of patching, ability to roll and store in the garage and overall they seem a little bit less expensive and more user friendly. Now a days I've moved up to a Sotar because its more of a performance boat and while I love it I would not hesitate to buy another hypalon boat, especially for my first rig. I tend to try an stay away from PVC because the lifespan of those boats aren't near what Hypalon and other materials are. Thats just my 2 cents on that.
A great website to check out with lots of used gear and is based in the four corners (mainly western CO) is mountain buzz. Here is a link to their used gear section:
http://www.mountainbuzz.com/swap/showcat.php?cat=3
Another great website just for inspiration : )
http://www.whitewatercampsites.com/
Permits as you know are the biggest challenge but their is a hierarchy to those with rivers like the Middle Fork Salmon, Selway (only allows one launch a day), and Grand Canyon seeming to be in the top. There are a ton of runs where it is easy to call in and get cancellations and there are still some outstanding rivers that do not require permits (especially in Oregon).
Let me know if you'd be interested in getting out. I've got spare gear. The dog thing may be a deal breaker for you but the offer stands. Any other questions let me know