Freya, I've got several brown rats like the one in the photo. They look similar to a wild rat but the wild rats here have more grey in their fur. I think the brown rats are called agoutis. Although they aren't in the pictures, I also have two pink-eyed caramel and white rats. One of them constantly rocks from side to side but seems healthy otherwise. All up, I've got 23 pet rats (7 girls and 16 boys).
One day, I'd love to get a russian blue and a russet rat but think they are quite rare. I had a beautiful pure white pink eyed little female last year but sadly she escaped while I was away for a couple of days and had somebody come around and feed them.
It's certainly possible to get angora (fluffy) rats and hairless or tail-less rats but I haven't seen them up here. The most common varieties in pet shops here seem to be the black and white or caramel and white hoodeds. I wonder if it's possible to get brindle or dalmation rats. They would be very pretty. You can get tan/black brindle (or tiger) mice.
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Break out you Western girls,
Someday soon you're gonna rule the world.
Break out you Western girls,
Hold your heads up high.
"Western Girls" - Dragon