I chose to build mine myself because I wanted the satisfaction of creating something, but also because I wanted to learn about bike mechanics. If you want instant satisfaction, go for the BD route.
Just be warned, if you decide to build your own, it's very easy to go over your budget. It helps a lot if you get a frame that has a headset, pedals, seatpost, stem, saddle, etc that are in good condition. This will save you some money to get nicer cranks or wheels.