An enthusiastic second here for the Wind Rivers! One of the most beautiful places on earth, IMHO!
The Highline/Fremont Trail is approximately 80 miles end-to-end from Green River Lakes to Big Sandy Opening, with no sidetrips. There is a shuttle service in Pinedale, WY, through the Great Outdoors Shop. Start at the north (GR Lakes) end for easier altitude acclimatization. If you want to do sidetrips (and, as mentioned, Titcomb Basin and Cirque of the Towers are almost mandatory, even though pretty crowded), you can start at Elkhart Park or do two loops, one at the north end from Elkhart Park and one at the south from Big Sandy. However, plan to take it really easy the first few days until you get used to the altitude. 2 years ago, I could do only about 4-5 mile days the first 3 days out of Big Sandy. Your mileage, of course, may vary! From Green River Lakes, you start at 8,000 ft. and take a couple of days to get to 10,000 feet. However, it also takes that long to get to the good scenery. From Elkhart Park or Big Sandy, you start at over 9,000 feet and are above 10,000 feet the first night.
There are several other trailheads, not as popular and not quite as high as Elkhart or Big Sandy.