I would say either a Nikon or Pentax. Mainly because both use the same lens mount today as they did during the days of film. This allows you to spend considerably less on lenses. I'm inclined to say to stick with Nikon over Pentax since you have aspirations to go pro. Nikon and Canon are the only brands making professional DSLRs and lenses (yes, Sigma makes pro-level lenses too, but not DSLRs). So while the Pentax K-50 is a better camera than either entry-level body from Canon or Nikon, in the long run it'll be better for you to just stick with one brand.
Since your budget is low, I would suggest buying a used body and lens. Put more emphasis in the quality of the lenses than the body. Here's some good lens options for the various types of genres that you've mentioned:
STREET: Traditional street photographers either use a 35mm or 50mm, but since you're likely to be using an APS-C format camera, you need to divide those numbers by the crop factor of the camera which is 1.5 for Nikon and 1.6 Canon. You'll want a slightly wide lens for street work and you'll want a fast lens. To keep the price down, and to get a larger aperture, you'll want to stick with a prime lens as opposed to a zoom. The Sigma 18-35 f/1.8 is amazing lens, but at $900, it's not feasible at this time. So, stick with either manual focus lenses (very cheap) or just get a simple pancake lens like a 40mm.
Don't be too concerned with image quality. Your main goal now is to learn the technical and artistic sides of photography. The photos that you make now won't matter, so don't think that you need "good" gear to get good pictures, that's simply not true. Your decisions are responsible for making a great photo, not the camera/lens.
PORTRAIT - A decent portrait lens is 50mm or a telephoto zoom like a 55-200. There are definitely better lenses than others. Having a lens with a larger aperture like f/1.8 of the 50mm, will produce a much larger amount of background blur. This is, along with it being cheap, makes the 50mm f/1.8 a very popular portrait lens. Remember, you can lower the cost of lenses by getting used manual focusing lenses.
LANDSCAPES: You want to have wide-angle lens such as 10-20mm. In 35mm format, a 28mm is a good starting point for wide-angle. However, the 24mm, while it doesn't seem like a big change, is significantly better. Those few extra mm makes a big difference. Wider the better. So a 10-22 would be a good choice. Getting a used 24mm or a used 18-55mm kit lens would be good enough to get you started.
You have the option of buying primes for all of your needs, but you can lower the cost of your kit by getting a single zoom. The 18-55 kit lens will do you fine for street, landscapes, and portraits. While primes can be better (e.g. allowing in more light, better blurred backgrounds), a simple zoom will definitely allow you to get acceptable shots and allow you to learn about photography.
Any DSLR will be a good choice as there are no bad cameras. If you can't take a good photo with a DSLR, then it's your fault.