As to RMNP, route depends on which side of the park you want to be.
East/Estes Park side is far more popular, and waaaaay more crowded. Reservations inside the park are a must at Moraine Park and Glacier Basin, the 2 most popular in-park campgrounds. Use the reservation window rapidly, sites book quickly. Commercial campgrounds will also require a reservation in most cases throughout the season.
West/Grand Lake side is not a popular, and a lot less crowded. Not to say there aren't crowds...there are. Just less than the Estes side. And the only in-park campground is Timber Creek, which is very nice and is first come/first served all season - no reservations at all. There are also some very nice commercial campgrounds just outside Grand Lake, and quite a few USFS campgrounds around Lake Granby and Shadow Mountain Reservoir.
As to routes, some of the routes mentioned above from other posters will work just fine. A slight modification here and there gets you to the west side from Moab. Unless you're a skilled/experienced mountain driver, I DON'T recommend taking Trail Ridge Road between Grand Lake and Estes Park or vice versa. Even with the caveats about no shoulders, and extreme drop offs, over the past several years the increase in popularity and thus traffic has been insane. It's getting less pleasant in a SUV or truck, never mind in a big rig pulling a toad. Pick a side, stay there, and use your toad to go between the two.