I mean, what is the TCT, maybe 40 miles from Phillips Pass? Less from the Tram. I did a three-day section of the TCT several years ago. At that point, the sum total of my backpacking experience was:
1) A college trip to the Smokies in March where I got badly hypothermic, carried sixty pounds, and wore cotton, and
2) A three day trip up Kings Peak, which I did immediately prior to driving to the Tetons to start the TCT.
I was the noobiest noob there is. I survived. I had a blast.
Not to diss on anyone here (there's a TON of collective experience here, and I'm certainly not the elder statesman of the backpacking world), but I'd feel very comfortable recommending at least a portion of the TCT to someone as a first backpacking trip. It's really hard to get lost, the effort/reward ratio is top notch, and information is plentiful. And I'd argue that there are plenty of bailout options. Granite Canyon, Death Canyon, and Cascade Canyon. At the end of the day, you've got to start somewhere. And while the Tetons are no joke, it's not like we're curing cancer or climbing Everest here. Do your research, plan modest days, spend a couple days at altitude before you start to acclimate, carry suitable rain gear, and you'll pretty much be fine.
But more to the point, the best way to set yourself up for a long, enjoyable "career" as a backpacker, is just to get out on your local trails, even if they're not the Tetons. Get the reps, not because you'll die in the Tetons if you don't get them, but just because... it's just plain fun. Stoked for you man!!!