First thing to get sorted out before you venture into buying a camera is to know what you're going to take pics off and know what you are going to do with them. This might sound daft but if you're going to be going out looking for photos of deer that are 50+yards away and intend getting the shots printed to 18"x12" then you are not going to get great results with an average compact, even if it has got 14 mega pixels or higher. For these kinds of shots you will need to have some pretty expensive gear, including decent long lenses.
If you want to take decent record shots of the day with the odd scenic as well and have them printed at up to 10"x8" then just about any branded compact will do a decent job. Don't be drawn towards the one with the biggest pixel count. In the world of compacts the more pixels there are on the sensor the more digital noise they generate when trying to get shots in bad light conditions (generally the dawn/dusk light we tend to be out in).
Waterproof is good, but not absolutely essential. If you have a decent inside pocket in your jacket it should keep the camera well enough protected.
What to get then?
Nikon, Canon, Panasonic, Olympus are all good brands to pick from. Don't spend more than a couple of hundred quid, because as a beginner you will not get the use out of many of the more expensive camera's extra features, and by the time you have grown out of the entry level camera there will be much better ones available for much less than the more expensive ones at the moment.
Make sure that, whatever one you get, it runs on a rechargeable battery and not AA's or AAA's.
I find that I tend to take deer photos when I'm out with the camera looking for deer photos and not stalking to kill. When I'm stalking I tend to take stalking photos and leave the wildlife stuff alone, simply because doing both compromises both
Anyway, hope some of this helps you