Hello, Georgios, and welcome to the Cameralabs Forum!
As the video showed, using a cheaper, older DSLR that maybe doesn't have as much features but putting on some good glass, will get you much better results than getting an expensive pro body but mounting some cheap, soft lenses. I like to say that a photo is made up of three parts, the camera body which accounts for 2%, the camera lens which accounts for 8%, and the eye of the photographer, which accounts for the final 90%. What good is having all this expensive gear if you're not a good photographer, or just don't have the enthusiasm needed to take a good picture? If I could quote Ansel Adams, "There is nothing worse than a sharp image of a fuzzy concept".
Anyways, the D5000 uses the same imaging sensor as the D90, but the D5100 uses the new 16 MP CMOS found on the D7000. Overall, the D5100 will get better image quality than the D90, but they're still pretty comparable. If you're worried about the 4 MP difference, it's not a big deal unless you're making enormous prints. Besides, being an older camera with an older sensor, the worse IQ is to be expected. I'd personally prefer the D90 over the D5100 for it's better construction and feature set, but if you really want the better IQ or the vari-angle screen, the D5100 is still an excellent choice.
Regarding the 600D, it's 18 MP CMOS produces a tad bit more noise than the D5100's 16 MP CMOS, but they're very similar overall.
If you're looking for some decent lenses, for Nikon the 35mm f/1.8 DX is an excellent, sharp lens and perhaps an upgrade from the kit lens such as the 16-85mm or 18-200mm would be a good choice. I own the 16-85 and I love it, it's such a sharp lens. You could also look at the 70-300mm for a telephoto zoom, and the 10-24mm for a wide angle.
Regarding Canon glass, I'm not too familiar with it, but their L lenses are definitively worth taking a look into (providing that you have the sufficiant funds