The Gateway GM5664 is a monster of a machine. Without knowing what type of video projects you are wanting to do I will try and focus on easy to use, professional quality formats and camcorders.
One of the most commonly used formats in the professional video production field is miniDV tape. There are both SD and HD camcorders that use this tape. To get footage into this computer you would need to add a FireWire (IEEE 1394) card to get the FireWire ports(also known as iLINK ports).
Flash Media and Hard Drive based camcorders are good, however the files that are recorded are a little tricky to work with in professional editing software. The AVCHD, although a great quality recording, is still considered a consumer grade format and not supported by higher end editing software.
If you want to experiment with FireWire editing first I would suggest the Sony DCR-HC52 found here:
http://www.bestbuy.com/site/olspage...If your ready to jump in with both feet then look at the Canon XHA1HD:
http://www.bestbuy.com/site/olspage...This camcorder will give you professional features such as XLR connectors for pro-audio gear, true white balance control, ND Filter and more.
To look at FireWire card options look here:
http://www.bestbuy.com/site/olspage...