If you are willing to spend at least $850-1000 (you said your budget is max $2500), it would probably be better to build your own pc.
A pc and a console are meant for different things. The Xbox One is a "cheap" alternative and has everything needed built in to game at 720/1080p, but not at max settings. It is made purely for entertainment. A PC can be made for entertainment, plus productivity. With a budget of $2500, you can easily build a pc that maxes out everything on a 27" screen (I'm assuming its 1920x1080). It really depends on what you are looking for in a gaming system. If you really want to play at ultra resolutions and are sensitive to performance drops and/or smaller visual details, go with a good, home-built pc.