I have the computer linked below, will it be able to run Fallout New Vegas? And if so will it run smoothly?
http://techwiki.hardwarecanucks.com/product/0MDEyNTY4/Asus-Essentio-CM1630/#spec
Ehh that's a little under powered for a gaming PC.
Look for something with a higher grade processor and graphics card.
For processors look for dual or quad core ones. For Intel the i5 and i7 are great processors and for AMD the Phenom II series are pretty good and a lot cheaper than Intel. As far as graphics cards go look for something that's around the range of an AMD Radeon HD 5770 or an nVidia GTX 460.
Here's a PC that is low end but still good for gaming ->
http://www.newegg.com/Product/Product.aspx?Item=N82E16883227314