I'd say go for a 360 if you want to get gaming goodness on the cheap without having to worry about meeting system requirements for the newer PC games.
I'd recommend building a PC over a 360 only if your budget allows for a powerful gaming system. Gaming PCs become obsolete VERY quickly compared to consoles which typically last a good 6 years.
$900 for the whole package isn't going to cut it for future games if you want to turn up the graphics and have a great gaming experience in newer games. If you've missed out on good PC games in the past couple of years, I'd go for a PC.
The keyboard and mouse combo is unbeatable for FPS and strategy games, but if you are into adventure, platformer, and party games (games you'll want to play when you have friends over), I highly suggest going with a console.
I agree with Mr T's suggestions. The 360 will be your best bet. The PS3 is improving it's game library slowly, but it's still not as good as the 360. The Wii's fun, but it's extremely basic with no HD resolution support, has a small game library, and poor graphics (an important factor to many).
Main rig: 1/2" ID Water Cooled Lian-Li V2000B, Abit IP35 Pro, Intel C2D E6750@ -3.4ghz 1.3375v, Mushkin 2gb DDR2-800 996576, one terabyte storage, evga 7900GS KO w/ Zalman VF700-AlCu cooler, Swiftech Apogee GT water block, Ultra X2 550w PSU
Laptop: Asus Z70VA, Pentium M 725 1.6@ -2.13ghz (pinmod), ATI X700 Pro, 1680x1050 native res., bluetooth, the works...