The I70 to Grand Junction route is the more traveled and better plowed. The other main way is Highway 50 to Montrose. It's a beautiful drive, but parts by the reservoir get icy and it's rather slow going. Having done both, I'd take the I70 to Grand Junction and head south from there route. Of course with either route you have to drive over Red Mountain Pass, which is a hold onto your hat type of pass. Especially from Ouray to Silverton. That 300ft drop with no guard rail and a six inch wide emergency lane does not leave much room for error. Take your time on that one. You could drive the 285 and around route, but that would add hours to your drive and the passes to Silverton from that direction are not much better. If it's really coming down the routes into Silverton will get closed fairly quickly, so I would try to beat the storm as much as possible Argo. I can't think of a better place to be stuck in than the town of Silverton when the roads close. Great 'effin town.
As far as places to stay. Their is the Hostel in Silverton. Most people stay there and I believe it is the cheapest option. Some good deals on houses can be found on VRBO too.
The other option is to stay in Ouray, which is a nice town too. Of course that means you have to drive the gnarly section of Red Mountain pass every day you go to Silverton.