This was taken with Canon XTi, Canon 420EX flash, and Canon EF 35mm f/2.0 (at f/2.2). In my opinion what you need is a prime lens with fast aperture (F/2 or faster), a DSLR, and a flash that can be bounced. Today, the cheapest you can get away with I think is the following.
|Canon Rebel XS 10.1MP Digital SLR Camera with EF-S 18-55mm f/3.5-5.6 IS Lens (Black)||About $450||Nikon D3000 10.2MP Digital SLR Camera with 18-55mm f/3.5-5.6G AF-S DX VR Nikkor Zoom Lens||About $500|
|Canon EF 50mm f/1.8 II Camera Lens||About $100||Nikon 35mm f/1.8G AF-S DX Lens for Nikon Digital SLR Cameras||About $200|
|Canon Speedlite 270EX Flash for Canon Digital SLR Cameras||About $130||Nikon SB-400 AF Speedlight Flash for Nikon Digital SLR Cameras||About $120|
|About $680||About $820|
Now, some might complain about this Nikon/Canon comparison. The Nikon has a nicer prime lens, as it is 35mm instead of Canons 50mm. The 50mm will be a little long to use indoors, but on the other hand, 50mm is going to create a nicer blur on the background when used at f/1.8-2.8 or so. Nikon has a cheaper 50mm lens, but it does not auto focus with the D3000 and D5000. Then the other comment would be that the AF chip on the Canon XS is maybe not handling f/1.8 lenses as good as the Nikon will. And if the XS is swapped for XSi or T1i, then the price for the Nikon will probably be less than Canon. Also, Canon does have a 35mm lens, but it is almost $300 and quite old design. If you really want 35mm on the Canon, I would probably go with a Sigma 30mm f/1.4 EX DC HSM Lens, but it is around $400. As you see, this can become expensive very quickly. You could try buying just the body and kit lens (18-55mm) and the external flash. That will be a nice start and will give you really nice indoor shots. And if you think that the background is not blurred enough, or the ISO is creating noise that bothers you, you can add the prime lens later to take care of that.
One note about the flashes for both cameras that I suggest here is that they are only able to bounce in the "landscape" orientation. If you use your camera in the "portrait" orientation, and still want to bounce the flash, you will need the Canon Speedlite 430EX II Flash or Nikon SB-600 Speedlight Flash. Both are around $230 or so. These can both tilt and swivel.
Anyway, you can also keep an eye on sites like Craigslist for used equipment. You can save quite a lot, but be aware, there are also many that sells at almost new prices, and might say "blank warranty card". But warranty cards are useless unless you also get a copy of the sales receipt stating where and when the camera was purchased. If you buy new at sites like Amazon, you get 30day or longer hassle free return right, and will not have a problem with the manufacturers warranty. I would recommend to buy from Amazon, with Amazon as the seller.
Another example of bounced flash with prime lens.