Essentially, IMO, you can either look for the latest and cheapest DSLR or not exactly the latest model but 2nd hand and a price similar to the latest but cheapest DSLR.
In other words, you can either get a new $1,000 DSLR (like Canon's 1000D, 450D) or a 2nd hand $2,000 DSLR at $1,000 or close. Whichever DSLR you're getting, it should suffice your needs as a starter or casual trigger-happy photographer as there's always better equipment.
On seperate note, achieving shallow depth of field DOF is one of the advantages of getting DSLR. That said, to achieve a more dramatic (very shallow) DOF, a lens with large aperture will give you a more pleasing result. For instance, the very inexpensive but good Canon 50mm f/1.8 only at ~$120. f/1.8 is the maximum aperture value you can use. The smaller the f/number the larger the aperture opening, the shallower your DOF.
Another way is to compose your shots by using the tele end of the zoom lens, say 18-55mm lens at 55mm. This is to get a compressed backgound to achieve the 'blur background' look. Also, the farther the distance between subject and background, the more apparent the background blur (bokeh) will be.
Hope this helps.