According to the EXIF data on that photo, that photographer was using a Nikon D700, a decent entry-level camera. Judging from the way it’s lit, he used on-camera flash (but probably not a built-in flash; more likely a separate flash like an SB-800 or 900) and balanced* that with the ambient light by using a moderately slow shutter speed (1/20").
You could buy the same kit (the D700 and most likely a kit lens, like a 28-80mm zoom) with an additional flash and you’d be well on your way. But I would recommend that if you do go this route that you look into taking some courses to help you familiarize yourself with the camera functions. There’s also a book called Understanding Exposure by Bryan Peterson that will help you make sense of that subscripted line below this paragraph, and help you understand how to work around the inherent limitations of your camera and get the best possible photos.
*By “balanced”, I mean that he likely metered the scene, and made the decision to allow the background to go about 1 to 2 stops darker than the people in the foreground.
He'd also be well advised to study the hell out of the instructions that came with the flash and consult the exposure tables, since most people -- and this applies especially beginners -- can't take a decent indoor photo with a shoe-mount flash (or a built-in flash) to save their lives. Lighting with a flash is not really intuitive. Most beginners seem to think that you stick the flash on top of the camera and that takes care of any and all lighting problems. It doesn't. I belive that the improper use of built-in flashes and shoe-mount flashes has ruined more photos than any other single cause.
If affordability is a prime concern, then maybe start out with a D3100 or a D5100, or if you prefer Canon cameras, give the Rebel T3i or T4i a look. Aside from Nikon and Canon, Pentax and Sony make good cameras. I’ve heard some good things about the higher-end Olympus DSLRs, but I personally revile that company so I can’t promote them. These days, really any entry-level camera is going to give you good shots and bad shots. It’s less about the camera itself and more about your understanding of it. My camera sucks compared to its competition, but I’ve still shot ad campaigns and magazine covers with it because I know how to work around its limitations.
Asking more experienced people for advice is a good way to go too - that's also taking advantage of the interwebs. dA forums are a great place to gain access to the knowledge of helpful people from all over the world