There are plenty of similar questions that demand highly and restrict things with a completely unrealistic budget. No wedding photographer would show up with a lens worth under $1000, nor with a single lens or a single camera. Getting a semi-acceptable wildlife lens is also not possible for much less than your entire budget.

There is good news and bad news: Used cameras provide great bargains because they drop in value quickly. However, used lenses keep their value. Therefore you will have to raise your budget significantly or buy the camera and rent the lenses. Now how to choose:

• DSLRs now all use CMOS sensors. You can go with a cropped-sensor (APS-C) or a full-frame one. Full-frame sensors provide lower image-noise but cost more and generally require more expensive lenses. I'd say a recent APS-C sensor is good enough.
• AF-Points. Many photographers use just a single one. They autofocus and recompose which becomes quick to do with lots of practice. However, when shooting subjects that move erratically, it wont cut it and here the more AF-points the better. Most cameras offer at least 11 but it goes as high as 61 which increases the odds of the camera keeping a moving subject in focus.
• Megapixels determine how big you can print. More megapixels equals larger prints. You need to figure out how large you want to print and that tells you how many MP are needed.
• Frames-per-second are how fast a camera can shoot continuously. When shooting moving subjects such as people, animals, birds, etc, it makes a huge difference. The faster you can shoot, the more chances you have to get the perfect photo at the height of action. Even shooting a relatively still person, the continuous drive helps get more shots where the subject is not blinking or has an un-photogenic expression.
• Viewfinder coverage: 100% is best because you see everything exactly as it will be shot. If you get anything less, you will will simply have to do a lot more cropping to account for unwanted objects (people's heads, hair, poles, wires, etc) at the edge of your frames. It can be rather time-consuming if you shoot a lot.
• Brand: For cameras it is a non-issue, for DSLR it is very important to choose the right brand as it controls which lenses you can use. Crucially for renting, very few stores rent anything but Canon and Nikon gear. Some do but they are the minority.

Now if you were to get the most of everything above, you would end up with a very expensive camera. What you need to decide is what is more important for you. Certain options appear only on some very expensive cameras. The great thing about DSLRs is that you do not have to buy all your lenses at once. You can buy a used camera and maybe you will be able to afford ONE decent lens for one of your needs. Then when you have more budget, buy the next lens and so forth. Until you do, rent the ones you need for each event.