Hi Lindsey,
I'm a Transam old-timer (crossed in '87) who lives in Boulder. I think you can do much better than 287 or east of 25. Those would be either high traffic or tedious. Perhaps you take 287 north out of Denver (avoid 93) but in Broomfield you want to take Dillon Rd to the west to Marshall Rd in the town of Superior. Marshall will drop you into south Boulder where you can follow the bike path network to the intersection of Broadway and 36 in N Boulder (goboulder.com for city bike maps). Boulder might be a good place to spend the night as there's a hostel or perhaps Lyons to the north.
From Broadway and 36 follow this map of the 100 mile route for the Buffalo Bicycle Classic
http://www.buffalobicycleclassic.com/images/assets/route_bbc_2010_100m.jpg. It's well thought out, scenic, and lightly traveled by cars. Once in the Masonville area you can head towards Horsetooth Reservoir and then hook into 287 just west of Fort Collins to start heading towards the Transam.
The roads north (and west) of Boulder are used as training grounds for many cyclists who compete on the international stage. It's great riding and it would be a mistake to bypass it and follow 287 (a 4 lane highway).
Good luck and enjoy. Brian.