You pretty much want to take I-70 to Frisco, CO, hwy 9 to Breck. From Breck you'll probably want to take I-70 east to near Denver where you'll take some route up the eastern side of the foothills, rather than trying to go up some route on the west side, since you'd be forced to go through Granby and Rocky Mountain Nat'l Park on Trail Ridge Road, to get to Estes -- not fun in a class C, nor would Berthoud pass be fun, though I've done it in 3 different class As (not to go to Estes).
On that east side you'll need, at some point, to get on U.S. 36 from Lyons or U.S. 34 from Loveland. So there are several choices on getting to one of those from I-70, either going north somewhere near Golden (CO 93 to Boulder) or going through Denver suburbs on the surface streets (not a good choice) or going all the way to I-25 then north to either the CO66 exit north of Longmont to Lyons or going to the U.S. 34 exit on the north side of Loveland.
One other thought is, if you take the U.S. 6 exit near Floyd Hill, to then take CO 119 north past Blackhawk to Nederland where you'd change to CO 72 (Peak to Peak Highway) to join CO 72, then past Allenspark to Estes, but that's not likely to be fun in a class C either.
Since I've not taken some of those stretches between I-70 and CO 93, particularly U.S. 6 near Floyd Hill or the Golden exit from I-70 to CO 93, perhaps someone else has better information. In any case, there'll be some steep spots and tight curves whichever way you go.