I picked up my Canon SL1 for a little over $500 with no kit lens, I already had another 18-55mm Canon kit lens as well as a well rounded collection of Nikkor prime lens. It did not come with a power adapter which ran something like $60. I also got Dragonframe (around $300) because I need live view for some more complex sequence with lots of minifigs on set at once.
I'm not sure if the modern cameras have fixed the aperture light flicker issue with constantly opening the aperture to get more light for the preview shot, but using a Nikkor to Canon adapter that ran around $35 has fixed that for me. Some of the more inexperienced film makers using DSLRs seem to have a bit of flicker in the footage they animate, I'm not sure if that is due to light clothing or uncontrolled light, or aperture issues.
Most of my Nikkor lenses cost between $80 and $250 apace. The more I understand lens length and the more demanding I get on myself for my own cinematography the more I crave new lenses. I just ordered a 105mm lens after borrowing someone's because I felt like I couldn't live without it. (That puts my collection at 18mm, 24mm, 35mm, 55mm,105mm, and 300mm prime lenses)
As far as dialog goes, I shot over half of my current project blind, and I can animate dialog all day without any sort of reference, if only my films were mostly dialog and light on spectacle I could get away without using a frame grabber at all, all you really need is a detailed x-sheet and to keep track of what frame you are on (that's what the ticker marks are on the side are for) the little (oo) next to words with arrows by them are how I want the hands of the minifigs to move.
The issue I have with web cams is not so much the quality (although the DSLR quality is hands down better) but being forced to only film with a SUPER WIDE lens. If you can justify the cost owning a DSLR is really nice for more then just animating, but associated animation related costs will run you around $400 on top of the camera cost.