Hi Lisa,
Definitely cheaper to build one, regardless what you choose but there is an element of risk in doing so. Incompatible parts etc. I'd recommend using Boards.ie's PC Building Forum for help, they are very good and very patient. Regarding what brand, the heavy duty gaming PC's are almost all universally custom built rather than off the shelf models. If someone was adamant they wanted one off the shelf, I would probably recommend a steam machine or alienware, but I think you'd make significant savings in learning to build yourself. As for the FPS, Purists will tell you 60FPS is what's needed at minimum. But it's very much how much is a piece of string. You can play the original Quake on my work laptop at 60FPS but it would struggle to hit 30FPS playing Cyrsis on high settings (forget ultra settings).
If I was buying a gaming PC tomorrow, my first thing would be establish a budget, go and get some PC Building advice, and then start ordering parts :) A customer built machine for more than 700 euro will play 99% of everything available out there without issue.
Hope this helps!
Dave