It depends rather on budget and what you intend to photograph.
I take macro photographs, wildlife, family portraits, mount the camera on a microscope, and do flash based high speed photography of things like water droplets splashing. It's not a hobby I throw money at though.
I use a Canon EOS 640. This is a mid-range half-frame digital camera with all the basic controls you are likely to need. I bought it when prices dropped just after Canon brought out its replacement. Like laptops you can save a lot of money by buying last years model. Photographic Magazines will often say what the latest wonder-camera is replacing, and then I looked up what people said on the web about the previous models.
The camera came as a kit with a fairly ordinary 18 to 55mm lens, which goes from a limited wide-angle view to a slight zoom, It's good for general purpose and 'get you started' photography. Because I needed one for a family occasion at the same time I also bought a mid-range flash which is perhaps half as useful as the Canon equivalent for a lot less money. Good enough for me though.
Later on I added a Sigma 70-300mm zoom / macro lens that goes from "wasp inside flower" to "bird on a chimney" type shots. The Sigma is an affordable lens. The image quality is good but more money will get you something that gathers more light, allowing sharper photos of fast moving objects like racing cars. Not important to me so I got the cheaper lens.
Then I bought a 50mm lens. These see the world much like the human eye. The optics are cheap to produce, so you get a very affordable high quality lens good, but not ideal, for portraits. I use mine with a set of macro rings to do extreme close ups of coins. Some kit cameras come with a 50mm lens. I don't think this is a good idea because the range of photo types you can take with it is quite disappointing.
I hanker after a real wide-angle lens, (less than 18mm), but don't really need one. Lots of fun to be had with them though!
If your girlfriend is likely to get seriously serious about photography, a full frame camera is a better bet. This is because full-frame cameras need full-frame lenses. Moving later from half-frame to full frame can be expensive if you have to upgrade a lot of lenses as well.
Photography is another hobby that can get you spending loads of money. A decent camera needs a decent tripod; perhaps a printer, with own-brand ink and good quality paper; slave flashes; lights; books; black cloth; stands; filters; camera axe; nude models; colour corrected monitor; exotic locations, software. (I use gimp rather than Photoshop for photo-editing. Whilst not quite as good as Photoshop it does most things. )
Might be best to start with a basic outfit and then expand it as your interests take you.
Some people get excited about Canon vs Nikon, vs Olympus. My experience is that there isn't much to separate them, at least at my level of interest. Lenses aren't interchangeable between different makes so choose one and stick with 'em.
Enjoy,
Dave