First of all, thank you for all your answers. I found them all very helpful.
I'd likely hone your list down to the D5000, Pentax KX Pentax KR, Sony A550 or Sony A580. The D3100 also, but between the two I'd like the faster frame rate of the D5000. The newer Pentax KR and Sony A580 will both push your budget to the max - the earlier A550 and KX are both still competitive and fine choices, though both the A580 and KR do have some nice evolutionary upgrades. If considering Canon, I'd try to work the 550D into my budget to compare to these others...the 500D wouldn't quite match the others in continuous frame rate or high ISO ability, which would edge it out for me.
I didn't notice the A550 anywhere but now I checked it out and it looks interesting. I will look into Sony once again. However the Canon 550D is just too expensive for me.
Also, I would personally not consider the faster frame rate of the D5000 to be a decisive issue. I'm not sure how much I would be using it. I think it's one of those things that would be nice to have but at the moment I've mostly tried taking photos which would not require such speeds.
The lack of AF with certain lenses did put me off Nikon too when I was starting out. While AF isn't a necessity, it sure is useful for speed and convenience the majority of the time.
Yes, it's also putting me off a bit. There is still the 35mm prime, which is a bit more expensive, but it will Auto-focus. For what photography would it be suitable? Indoor (such as churches and museums)? What else?
I feel like I'm moving away from Pentax as they don't seem to offer the lenses I wanted for cheap (e.g the prime lenses mentioned above). And as a beginner I know very little about the camera second-hand market and so I'm not sure I would want to go down that route.
So I believe my options are now Sony A550 (which I will look more into), Nikon 3100D and 5000D, and Canon D500. Out of the last four, Nikon 3100D seems to be the cheapest and newest and so I'm leaning towards it (though the difference isn't that great).
This brings me to my question. Since all the cameras I mention above are quite close to my budget, I won't be able to buy all the lenses I want. What do you think I should go for, taking into account my main interests? Should I go for 55mm-200mm lens? Would I need them? Or should I rather leave them for later and get a 50mm or 35mm prime? I don't know, it just feels a bit weird not being able to zoom in on a camera, but that might only be because I'm used to having it around.