I have hiked the Teton Crest Trail four times in the last five years. Yes, I can give the trail a high recommendation, a classic. I'm enjoying seeing the different in the same year to year. I like it as a cool down after a big trip in the Winds. I can go on auto pilot and just walk and look. The trails are superbly maintained and thoroughly signed, as you'd expect in a National Park. Navigation and footing are non issues (assuming a bit of competence). You see plenty of people, even in the backcountry, many with little experience, lots of enthusiasm and big loads. Camping is assigned by permit to a zone or lake. Some permits are given in advance and some are saved for walk in. Parts of the route are outside the Park and you may camp anywhere in those areas. I'm a walk in kind of guy with campsite flexibility and have had unfailing luck here. There are established sites. I've looked at every single one and slept in quite a few on my loop starting and ending at Granite Canyon, crossing Hurricane Pass and Paintbrush Divide, returning via the Valley Trail. Some are bare dirt log squares that tend to puddle rain on one side and are a little small for shelters with lots of lines. They are all scenic. Have you gotten the map yet? I suggest you pick your lake or zone by your desired milage or availability and if you really want the best spot get to the zone as early as possible to have the best choice. Death Canyon Shelf and North Fork Cascade Canyon are nice. I'd try to be there for peak flowers, because they are so fantastic. Bugs are not as much of an issue compared to some others spots nearby, The Winds for example, due to unfavorable (for bugs) topography, not so many marshy spots. I hope this is of use and that you have excellent time where ever you go.
All Best, Eric