1. Every camera is always a compromise. For example, if you have a large heavy camera, it most likely will produce outstanding image quality, but it will also be hard to move around and it will be very expensive. Remember, a camera you dont have with you when you see the possibility for a picture is USELESS in this moment. Photography is impossible without a camera. Thats why I myself are constantly looking for the perfect compact camera, even if I now most of the time have my D600 with me.
2. There is a ton of cameras around. Each with their advantages and disadvantages.
3. There are TWO important aspects of photography:
a) The technical side. If you want to be a good technical photographer, you need a camera that allows you to control the photographic parameters well. You want to learn about the exposure triangle and all the other things.
b) The art side. Knowing the technique will help you to make more pictures, and pictures of different kinds. Knowing the art side of photography, composition, will allow you to make stronger pictures, no matter the camera.
c) The more you have mastered both sides of photography, the more important is of course creativity.
4. A good general purpose camera would be for example the Nikon D3100 (or, for a very useful flipscreen, the D5100) with the 18-55mm kit lens. This lens produces good image quality if stepped down to f/8 over most of its range, and it allows to do some macro photography (maximum mag 1:3.2). You might also want to add a SB700 (or used SB600, or some good Metz with Nikon i-TTL support) flash soon.
5. Another possibility, but its hard to tell: you want a camera and stay with it for years to come. Then you want a camera that doesnt limit you in photographic choices and gives you good control over the photographic process. The lowest choice for that would be the D7000.
6. As already mentioned, the choice between Canon and Nikon is mostly taste. I myself for example put high priority on low light performance, so I went Nikon. Canon isnt too bad in low light, either, though.
[...] If you have a $10K budget, then the best camera to get is a D4. [...]
Really, really not. The D4 is a specialized camera for sports and news photographers that need ultimate robustness and reliability.
Even most pro photographers are better off with the D800 (best Nikon for video), D800E (best Nikon for studio/landscape/best resolution), or D600 (best Nikon for general use, specifically thanks to low weight and fast switch between two configurations possible, but also ugly oil on sensor problem and small AF area).
For an absolute newbie, the highest I would buy is the D600, because thats the last Nikon with the good old green Auto mode. Canon shooters have it better with that, the Canon EOS 5D Mark III still has this mode, while the Nikon D800 does not.
With a budget around 10k$, a good setup could be, for example, 2x D600, AF-S 16-35mm f4 VR, AF-S 70-200mm f4 VR, AF-S 50mm f1.4 (for a cheap and small low light lens, or alternatively the new Sigma 35mm f1.4), AF-S micro 105mm f2.8 VR (Macro photography), SB700 flash (possibly 2 or 3), plus good backpack (for example Lowepro Flipside 500 AW), good straps, tripod with good ball head, filters etc. That allows you high image quality, low weight (for a full frame DSLR, anyway), the ability to carry that stuff all day, and good flexibility.