A regular panel mat would be fine. I have attached a picture of one below. Panel mats are mats that fold and unfold. Check with your club first to see if they have any mats for sale for the holidays.
Things to consider:
Size: 4'x8' or 4'x12'
Thickness: 1 3/8" or 2 1/2"
Firmness: Regular or Mushy
Color: Solid or Rainbow
Velcro: None, Ends, or all 4 Sides
Type of Vinyl: Standard or Heavy Duty
Remember that the mats can connect with the velcro, so you could always start with an 8 foot mat and buy another one in the future for a total of 16 feet. If you would like to connect the mats side by side, then make sure you get velcro on all 4 sides.
Standard panel mats are 1 3/8" thick, thicker mats are available for additional safety. Remember, the thickness of the mat will not matter if a child is not supervised. If you land on your head you will get hurt with either thickness.
Some companies sell mats that are softer (preschool mats). Most people prefer the standard mats.
Heavy duty vinyl is the kind of vinyl on school mats, the old tan and blue ones. This is much more expensive.
Make sure you check the shipping deals.
Here are some links:
http://www.resilite.com/ - Basic mats for home, check their Christmas mats.
http://www.mancinomats.com/gymnastics/index.xhtml - Basic home mats, check their holiday promos.
http://www.supply.powaygymnastics.com/folding_mats.php - the AAI dealer by us, AAI is top of the line Olympic quality equipment.
http://www.unitedathletic.com/TumblingMats.html - the maker of the mat pictured below
Now that I have said all that, we sell Resilite mats at our club during the holidays. It is a quality mat for the price.
If you need any help beyond that, call Tony at the Poway Gymnastics link above and tell him Justin from Gyminny Kids sent you. He can help you out with whatever you need. We buy most of our club equipment from him.