Upvote:3
I personally prefer a backpack because I can sort things into different compartments and everything zips up. There's also a handy exterior pocket or two for a water bottle. If you get a smaller size, college student- or commuter-sized backpack, and don't pack it full, United's not going to care if you're off an inch in the measurements.
If I were going to use a tote bag on a trip, I would get one that has a zipper on the main compartment. Otherwise, it's too easy for someone to dip their hand in and snatch something.