Planning a trip to Grand Teton Natl. Park

Hey everyone, me and a buddy of mine are planning on going up to Grand Teton this July for 5 nights. We are both college students so we are trying to be as cheap and minimal as possible. Our idea is to do the backcountry camping since it is only $7/night per person plus the permit fee. What we are hoping is possible, is to hike the trail, come back to trailhead, grab camping stuff, get to backcountry site, set up camp for night, and start over at another trail the next day. We are trying to use the stuff we have without spending a ton of money on super light stuff, so we can carry it to the campsite without actually backpacking with it on all day, and also not leaving it unattended.

Main questions are:

• Can we hike the trail, then go back to the car to grab camping gear, or are backcountry sites too far from trailheads?
• Are there dispersed campsites that are right on trailheads?
• Would it be better to stay on campsites? (Personally, I want to be far away from people lol)
• Are there any "must-knows" you have for me before we do this?

We are still trying to figure out some of the trails we want to do, but I have a map that outlines all of the backcountry camping areas and where they are, so I think it should be pretty easy to narrow down.

I really hope this doesn't make me sound stupid, I am just having a hard time mapping everything out and everyone I have talked to has just 100% backpacked in these areas.

Thank you for all of the help!