From Lake City to the top of Engineer pass is easy. I saw a ford minivan go to the top this way. The other side , to hwy 550, is tougher. I wouldn't recommend that you do that side.
Lake City to the top of cinnamon pass is fairly easy. A buddy of mine did it on his RT. But there is a long steep loose rocky downhill that goes into the ghost town of animas fork. Silverton to Animas fork is fairly easy. A few swithcbacks and a little bit of rocks here and there.
Ophir pass is mostly easy. Rocky at the top and going toward Telluride for a little ways. Go slow and pick your way through.
Imogene pass from ouray is moderate. The pic above is going up to Imogene. Imogene pass from Telluride has narrow steep swithcbacks with straight down drop offs.
My definitely DON"T DO list for an inexperienced dirt rider is --
Black Bear pass and Poughkeepsi gulch. Jeep rental places tell you to stay off these.
Corkscrew gulch is steep and narrow and slick with drop offs. California Gulch is rocky towards the top. And when you get to the top you either go back, or go down poughkeepsi or corkscrew.
An easy scenic ride is Last Dollar road. It goes north by the airport in Telluride. Scenes from True Grit were filmed there. When you hit the HWY turn right to ridegway. Just a little ways north is Owl Creek pass. Another easy scenic ride. More of True Grit was filmed through here.
Almost anyplace that you walk into in that area will have good maps for sale. Trails Illustrated are some of the most detailed maps.
The scenery in this area is incredible. Have fun and take lots of pictures.