For $800 you wont be able to get all you want. For example you can get KIT DSLR $6??ish price varies on XSi you can follow it. Then you'll still have the cost of SD card ($38 for 16GB Transend class 6), ($40ish) bag. That is all you will be able to buy for under $800 to get started. Later you will want a good flash ($220ish) and then a telephoto lens ($250ish) if you are willing to slowly upgrade go DSLR if you want it all now go with super zoom. I my self chose the slow rout and bought a T1i kit and am going to order a flash 2nd and later some lenses.
most of what you are looking for will require a telephoto lens or a flash. you can save alot of money and get some decent shots with a super zoom like a canon SX10is or SX1is but if you are willing to upgrade slowly go for the DSLR.