What is your definition of "Unsupported"?
The CT is 486 miles and packs a lot of elevation change. The JMT is a good warm-up for the CT. The average pace is 5 weeks at 16 miles per day. The only one I'm aware of who ever did the CT straight through without resupplying was Coup, the owner of Golite.
Do you really think you can carry that much food? Remember, it's not just the weight but also the bulk which must be overcome. If you have a car, you could cache supplies along the trail at convenient road crossings (and hope nothing happens to any of them). However, the only truly inconvenient off-trail town stop is the Creede/LakeCity area. Definitely read PMag's guide; he's the "go-to" expert on the CT. Also read the current and past years' threads on the CT Forum at trailforums.com so you know what you're getting into.
If you want to do a truly unsupported long hike, and since you've not hiked out here in the west before, let me suggest that you start with the JMT. If you can do those 212 miles, 8 of the 9 PCT high Sierra passes, and Mt Whitney continously without resupply or town stops, and without altitude problems, then try it on the CT next year.
Re: bear canisters - yes, you'll carry one the entire way on the JMT, but you only MUST use them in certain defined areas, and even in most of those areas, you have the option to use the bear boxes provided at specific campsites (this restricts your mileage and camping locations, and they're not all are within a day's walking distance of each other). Besides, you walk right THROUGH Red's Meadow with it's store and PO; ditto Tuolumne Meadows, and going SB,Muir Trail Ranch is an easy 3/4 mile off-trail and 1.5 mile back.
Another shorter western option would be the 165 mile Tahoe Rim Trail (TRT), which is a perfect loop, so there are no concerns with how to return to your car.