We were just in Durango for a few days.
If you have a hose, most gas stations will let you fill up. Where you dump should be potable water. I have been in Santa Rita Park, I just don't remember the dump station.
Durango has full services, Autozone's etc. They have a Walmart etc. Walmart is probably your best bet for miscellaneous camping stuff. There are hardcore backpacking stores in Durango.
There are two campgrounds north of town, Rose something or the other and I believe United. The last one we stayed in was United and that was probably 13 years ago.
Mancos, has a good fuel stop on the east side of town near a liquor store and at the intersection with 184. You can probably get water there as well.
Remember you are in the west, things are still a little different, maybe a little more friendly.
