What is your budget, and what are you looking to spend?
Flipcams
I took this using a Kodak zi8 that I bought for less than $100. The remote is $10, and if you leave it plugged into a wall outlet then you don't have to worry about changing batteries. Add another $20 for 25 foot HDMI cable to hook it up to a HD TV, and it can play videos back at up to 1080p, all controlled from the remote.
www.youtube.com/watch?v=ZeJkKtpej9Y
Videocam
Canon Vixia G10 are great, but last time I checked B&H they wanted $1,100. I ended up buying a Canon Vixia M40 instead, and used the difference to buy a rode video mic and Canon t2i DSLR setup.
Here is footage from the Canon Vixia M40.
http://www.youtube.com/watch?v=xO0QPFxT4KE
DSLR
My Canon t2i has the same megapixels and controls as the t3i. Stock firmware limits recording to 12 minutes in 1080p. If you're recording a single game of 8-ball, 9-ball, its fine, but not for longer games like 1 pocket or straight pool, unless you like pauses.
My Vixia M40 is alot easier to use than the DSLR, I just hit the record button. On the DSLR, I end up tweaking ISO, shutter speed, aperture and changing lenses. Before getting a DSLR, I never knew or cared about photography. Nowadays, everytime I walk into dark poolroom, I ponder selling my fellini, jack justis, and murnak cases so I can buy a low light f1.2 lens.
If you're looking to make movies, DSLR is the way to go. T3i big brother is the Canon 5D Mark II. Footage from Marvel's Captain America and The Avengers has been shot on the 5D, and the cartoon ParaNorman was filmed entirely using it.
For my next video camera I would look into the the Panasonic GH2/GH3. People swear the video quality is on par with the 5D, but without the 5D pricetag.