I also would split the question down in two. Firstly the camera (limiting my choices to Nikons current range of DSLR's).
Firstly DX format cameras. These have an image sensor roughly half the physical size of a traditional 35mm negative. This means that the focal length of any lens which is measured in full frame or 35mm terms, will give you a magnification of 150% over the lenses stated value. In other words if you put a 50mm lens on a 'Nikon' DX camera (other manufactures DX bodies have different sized sensors, so the effective magnification value is different) the amount of the scene that you will see through the viewfinder is the same as using a 75mm on a FF camera. Pros and cons of that situation? Well very high magnification lenses (400mm or more) are very expensive, so if you're shooting involves being a long way away from your subject, a DX body gives you an instant 50% advantage over FF. The down side? Well as you can imagine if you want a very wide angle lens, (15mm or less say), then the extra magnification of DX becomes a hinderance, as a 10mm becomes a 15 etc. There are other pro's and cons such as depth of field, and low light performance, but they are discussed elsewhere. Sensors are expensive, and so because DX cameras have smaller ones, they are cheaper to produce and therefore DX cameras for this reason (and significant others) are cheaper to buy than FX.
Nikons current DX line up is:
D3100, replacement for the D3000 still available, suitable for anyone who is buying their first DSLR, has only ever shot in full auto, and doesn't know why you would choose anything else. Has an on screen help mode that explains what affect altering the various settings will have on the picture you take. Very useful for those making their first steps in photography.
D5100, replacement for D5000 also still available, currently Nikons only DSLR camera with a swivel view screen. Similar to the D3100 in that it is very easy to use and has pre-programmed 'scene' dial options, that assist with making setting adjustments for the most commonly encountered photographic situations.
D7000, replacement for the D90 which can still be bought new. Made with tougher materials and metal under it's plastic skin. Also has improved weather proofing over the lower models in the range. When you get to this model the mode dial on the right shoulder (when looking through the viewfinder) has been replaced with an LCD screen, which gives the user much greater information on the settings that the camera is using. The available options in the menu are increased over the the lower cameras and the ability to alter how they are accessed and to assign functions to buttons on the camera is increased. Other benefits include the ability to use older Nikkor lenses, fit a battery grip for extended battery life and easier vertical shooting, and wireless CLS flash activation, make this camera much more suited for the experienced or up and coming photographer.
FX bodies are currently the D700, D3s and D3x. If you don't know what these offer and why you would want them, buy a DX! Lenses for FX cameras tend to be more expensive.
Some DX camera bodies can be bought as part of a kit, which includes the camera body and a lens or sometimes two in the box. Hence the term 'kit lens'. These can be useful lenses to begin with, and will certainly get you off to a good start if you are starting with nothing. The benefit of buying a camera and lens kit, is it saves money on buying the items separately. If you already have some lenses though, it may be better to buy your camera 'body only' and then decide which additional lenses you need at a later date. Kit lenses are generally made to a price. This means they will be made using cheaper materials (plastic rather than metal), and will be "slower" meaning they have have a smaller maximum aperture. What does this mean? The aperture is the 'iris' through which the light is allowed through the lens. The wider the aperture the more light that can come through. This value is described as a 'f' stop. The lower the 'f' value the more light that can pass through the lens. Better lenses have larger maximum apertures, because this means that they can be used in lower natural light levels for a given shutter speed/ISO combination. I won't go into detail on the other benefits here, but as you increase the size of the aperture by one full 'f' stop, the lens lets in twice as much light as the stop before. This has a corresponding effect on the shutter speed and sensitivity (ISO) that can be used by the camera to produce a well exposed image. If any member of the forum would like to pick up the batton, and explain how these three values interact with each other I'd be obliged, as I'm now getting RSI in my fingers for typing so long :-) The general rule is to buy the best lens you can afford, as unlike camera bodies, they hold their value for much longer, are updated far less frequently and have the most beneficial effect on your photography. Zoom lenses with 'constant' maximum apertures are also generally considered better, but are more expensive than ones who's maximum aperture changes with the lenses focal length. This is not an issue with a 'prime' or fixed focal length lens.
OK guys, what did I miss? Please feel free to expand upon or correct any inaccuracies that I may have mentioned :-) I'm not sure if Adamz wanted us to go quite this far back to basics, but hopefully a newcomer will find the above useful?