In addition to the camera, you will need a camera bag; this protects your camera when you're not using it in case it gets bumped, dropped, rolls around on the back seat, etc. One cool feature a lot of bags have now is an integrated rain fly that folds into a small pocket on the outside, so if it starts to downpour, just unzip the pocket and fold the waterproof fly over the bag. I think water protection is important but you can simply keep a small trash bag or a couple plastic shopping bags in one of the pockets. This should be organized to hold he camera, camera manual, the MANUAL, extra memory cards, room for one additional lens (commonly overlooked, you will probably get another lens and if you don't, throw your game boy, bible, pocket reference, maps, survival kit, cab fare, etc...), usb and other cables, cleaning accessories, rear lens and body dust cap, and any accessories you plan on buying in addition. Expect to pay about $50 for a quality bag.
Memory cards are so cheap (relatively speaking; this same card had a MSRP of about $200 in 2010) that you should buy the fastest class 10 you can afford, for example the 32GB Sandisk class 10, 45 mb/s is only $30-40 and are reliable in my experience. Have a back up card, too, even if it's just a couple GB because you always run out of storage when you need it the most. $50-$80.
Lens cleaning accessories should be less than $20.
I found that a lens hood and circular polarizing filter come in very handy and are probably the only accessories I would recomend a beginner buy with or be the first accessories to get after buying the camera. A hood is about $10-$20 and a decent polarizer should be about $100-$150, or $110-$170.
What medium will you record the images to? Always keep hard copies- don't just upload all of the data to your computer and wipe the memory cards, too much can go wrong. Either burn the files to a DVD, an external drive or just keep the SD cards and buy new ones as you need to. I would estimate about $30 for a new memory card or package of DVDs or $80-$200 for an external drive.
A lower estimate would be about $160-$200, the upper estimate being about $400-$500. With a budget of $800 for everything, I would assume a lower end of camera accessories, leaving you with $600-$640 for the camera (and, obviously, $300-400 for the camera on the upper end).
Something like a t3i would be practical with that price point and they are good cameras, but on that side of $1,000 I would be inclined to buy a super zoom or a nice point and shoot and save the rest for a better camera down the road.
In other words, I got a Canon powershot SX110 IS to start out because it's never bad to have a camera and at $150 it's not a big deal if I wasn't interested in taking photography further. I used this for about two years before buying my 60D and in full manual mode, I was able to take some really nice shots. Still keep it in my glove box for when I don't have my DSLR or don't want to risk getting grinder dust, sparks or slag in or on it.