Well, that bestec PSU is a standard ATX psu, so I'd say it is safe to assume that it will fit in your case. The only part I am worried about is whether or not emachines is using any proprietary motherboard connections. I just did a bit of googling, and the best info I could find said that the "newer" emachines can use standard ATX psus no problem, but no specific info on your particular model.
I'd go to their live chat:
http://www.emachines.com/support/options.html and ask them directly to be sure.
Assuming a standard ATX will work, here is a great one for $40. It has over 30amps on the 12v rails, and 400w of juice which will be PLENTY for your system:
http://www.newegg.com/Product/Product.asp?Item=N82E16817104953