Spring is great, but it can still snow in spring and the run off can block some of the trails east of town. Summer is a little tough but if your going to be mostly in an air conditioned truck it doesn't matter that much, just plan on a siesta from 12-4 every day. Winter is pretty mild. If you can get out there before Easter that's best, since Easter marks the beginning of the heaviest tourism season. Fall there is awesome!
As far as time to spend, 5 days gets you a good taste 10 is better; you can easily spend 5 days just in Arches or touring landmarks, driving the desert, or hitting hike/bike trails without ever seeing a 4 wheel drive road. Dedicate a day for arches, a day for other landmarks, and a couple days to trails (hike, bike, climb or offroad) and a free day to do more of what you liked from the first few. There is such a huge amount to see and do, thousands of years of human history, tourist traps, scenery, geology... pick a few and know you won't hit it all.