Ok, you also need one of the AC to DC power blocks they show as related items to make that power supply work. The board you show is a 12V DC input to +12 -12 +5 regulator board for the components but doesn't actually change the AC house supply to DC.
There isn't enough info on the battery pack or the ac to dc block to know for sure if that battery will work. The best thing to do is wait till you get the power block and bring it with you to buy a battery. Any universal external laptop battery should work, hard to say about the battery you linked to. Be careful that the plug polarity is correct before plugging any battery into your power supply. The polarity should be on the AC to DC power block when you buy it.
Another concideration is how many amp hours the battery will supply. I haven't looked into this personnaly, but you may want to check what external laptop batterys provide for amp hours that are expected to run a laptop x hours and compare that to the amp hours of the battery you linked to. The DVD battery may be cheaper, but if it doesn't last long enough, it may be a waste of money even if it will fit your power supply.
Oh, if you don't plan on running this off house power, email the sites support for the polarity needed for the dc to dc power supply input plug. It will be one polarity for the center and another for the outside of the plug. If you plan to use this in a car primarily, you could skip a battery and get a cord to plug into a lighter socket.