PC Setup for Small House with Child?

nzgeek asks: "I've been managing with a pokey Windows notebook for a couple of years now, and am desperate to get a decent PC for development and gaming. Problem is, our house is tiny and we have a 1-year-old entropy generator running amok. What's the best recommendation for getting a full-power desktop PC installed in our house? My ideal setup would be a mini-tower case hidden in a cupboard, with a remote LCD monitor, mouse, keyboard, and headphones. The keyboard and mouse can be done via bluetooth, and there is no problem with cable length for headphones. The major stumbling block is VGA connection for the monitor. Any suggestions on how to overcome this problem?"