Busker:
Be advised - the Denver REI is in downtown Denver; nowhere near the airport.
It is very easy to reach the Platte River on day one. The first 6.5 miles along the road in Waterton Canyon are essentially flat or only gradually rising, but you are out in the open, so start early if it's going to be hot. The next 6 miles are uphill under tree cover; the last 4.2 miles are all downhill, again under the trees. There is a great campsite at the top of that hill (on yourr left) butit is dry. Better to go all the way down to the river, where there are campsites across the bridge. Your body will thank you the next day when you're faced with the burned area in segment 2 (actually, almost ALL od segment 2 is burnt area.
Segment 2 is all uphill and out in the sun. You'll want an early start so as to reach the trailhead parking lot at the end without being fried. The only water in segment 2 is at the fire station near the road crossing. Your next water is a few miles into segment 3.
Breckenridge is 105 miles from Waterton Canyon and can be done comfortably in 6 days. Even if you think it will take 7 days, only carry food for six. The free Summit bus stops right across the highway and to the left at the end of segment 6. The little enclosed shelter is readily visible. If memory serves, the bus comes about every 45 minutes.