Fast telephoto lens?

Caporegime
Joined
12 Mar 2004
Posts
29,954
Location
England
I'm looking for a fast telephoto lens for shooting sports in an indoor arena, ignoring Nikon for now which are very expensive I have found these at a glance.

sigma 50-150mm f/2.8 EX DC OS HSM £564
Sigma APO 70-200mm F2.8 EX DG OS HSM £676
Tamron SP AF70-200mm F/2.8 Di LD (IF) Macro £487
Tokina AT-X 535 AF PRO DX AF 50-135mm f/2.8 Lens Nikon £275

Are these all compatible with my D5100 and are they of acceptable quality? IS doesn't matter too much because I can just improvise by using a wall, and the shutter speed will be around 1/500 sec anyway.

Those are all new prices from *******, I have no idea what prices are available second hand.
 
I'm gonna use my old 18x bridge camera to figure out what focal length I need, certainly can't afford Nikon's offering though!
 
After seeing that the 50-150mm is only APS-C, I think I'll have to get the 70-200mm, I don't want loads of vignetting when I upgrade to full frame and try to use the 50-150mm.
 
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