Raspberry Pi 2 on sale now at $35 | Raspberry Pi
$35 for the pi.
Use pretty much any mini USB cell phone charger for power supply.
Has HDMI, ethernet and 4 usb so you can use USB wifi dongle.
Download noobs image from the site and install OS of your choice to an SD card and that's pretty much it.
I simply toss them behind the TV but you can make a case out of an old Altoids, cardboard or even Legos.
https://www.google.com/search?q=pi+cases&espv=2&biw=1525&bih=1094&source=lnms&tbm=isch&sa=X&ei=1ZHqVPOwNoikNvm7gsgF&ved=0CAcQ_AUoAg&dpr=0.9