Two of us did the Teton Crest Trail late last August. We flew into Jackson airport, which meant we had figure how we were going to get from the airport, to/from the trail heads, and also meet a few other travel requirements.
After researching various options, including the cost of a few taxi/shuttle services we found on the internet, we decided to reserve a rental car to pick-up at the airport and spend a few days fishing and "touristing" after hiking the Crest Trail.
For us, a rental car was more convenient and flexible than trying to schedule in advance multiple shuttles to/from the airport, to/from trailheads, and also to/from town to pick up supplies that we couldn't carry on the plane (fuel, bear spray). Plus, at a weekly rate, a rental car didn't appear to cost a lot more than multiple taxis or shuttles would have cost. However, one shuttle trip was necessary as described below to start the hike.
We arrived at the airport about 3 pm, picked up the rental car, and stopped at Moose Visitor Center to get a permit for starting our hike the next day. We then drove into town for supplies, and also arranged for a taxi/shuttle service to meet us at Jenny Lake parking lot the next morning and take us to the Teton Village tram. Our trip included taking the tram to the top of Rendezvous Mountain, hiking to Marion Lake, continuing north along the Crest Trail, and coming out at Jenny Lake.
The next morning, we left the rental car at the Jenny Lake parking lot, where we were picked up by the pre-arranged shuttle taxi for the short drive to the tram at Teton Village (less than 30 minutes, as I recall). Four days later, we completed the trail at Jenny Lake, where we picked up the rental car. We spent a few days fishing and goofing off before driving back to the airport to fly home.
The taxi/shuttle from Jenny Lake to the Teton Village tram was about $30 or $35 total for the two of us and our packs.
As for bear cannisters, the park service requires that you use one and will loan it to you for free if you don't have one with you. I believe the brand was Garcia.
To plan for weather and trail conditions, we checked the Teton National Park website before leaving home. It has pretty detailed information on conditions for passes and trails in the park. We also checked the internet for Jackson Hole's 10-day forecast just before we flew there. Jenny Lake Ranger Station and Moose Visitor Center also have current forecasts posted and updated daily for hikers to check just before heading out.
However, even with all of those forecasts predicting great weather for our trip, with no snow reported on the passes, we still experienced a pretty severe thunderstorm during the second evening, including snow. Since we would be crossing Hurricane Pass the next day, the snow and thunderstorm that night caused a bit of concern about conditions going up and over the pass. Fortunately, the worst of the bad weather didn't last long, and the snow melted quick. The weather cleared up nicely, but it was still very windy and cool going over the pass.
This was in late August, by which time the passes were reported to be all clear. Earlier, in July, some or all of the passes along the trail might still be holding snow, and a fresh snowfall is always possible. A year earlier, in late September, we had a permit to go from Jenny Lake to Lake Solitude and out via Paintbrush Divide, but a snow storm the night before we were to start hiking caused us to cancel the trip. We drove up to Yellowstone and spent our time fishing, instead.
Best sources for learning conditions for your trip would be the park website and calling the ranger office shortly before heading for the Tetons. But don't be suprised if you do encounter snow, even if none is reported or forecast when you start the hike. We saw a few folks on the Crest Trail with ice axes. Even though they were only hiking the trail (the whole trail in one day!), they were prepared for snowy passes just in case.
Have a great trip! And just as a preview, here's a few photos from our hike:
Camp on Death Canyon Shelf:
Death Canyon Shelf, looking north:
Trail down to Alaska Basin:
Grand Teton from upper South Cascade Canyon
Cascades along South Cascade Canyon