That's good equipment for starting out. The 50mm/1.8 should be fine when starting out. Well, it is cheap. I used it for a year and a half before getting tired of it. Main problems with badminton - slower focussing speed and sometimes a bit hard to nail down the focus (in non-badminton shots). I think it's because the focus steps are quite large. I did get some good shots using it though.
Since you are only interested in the equipment for badminton, you really need to stick to the f2.8 or larger aperture lenses. Avoid any f4 lens because you'll be wasting cash. Can't stress that enough.
Sigma do not do any short range zoom lenses that have HSM.
I would think that HSM is important - the lens can focus a lot quicker with it.
I'd say stick with the 50mm for the time being. Kwun's suggestion of 85/1.8 or 100/2 are very sensible for the future.
Since you are only interested in the equipment for badminton, you really need to stick to the f2.8 or larger aperture lenses. Avoid any f4 lens because you'll be wasting cash. Can't stress that enough.
Sigma do not do any short range zoom lenses that have HSM.
I would think that HSM is important - the lens can focus a lot quicker with it.
I'd say stick with the 50mm for the time being. Kwun's suggestion of 85/1.8 or 100/2 are very sensible for the future.