What kind of fastener should I use to attach a mounting bracket to metal studs?
It depends on the type of mount.  If it's an articulating arm mount, the bending moment at the wall is going to be a lot higher than if you're doing a flush mount.  In that case the safest option would be to open up the drywall and put 2x4s inside the metal studs, and use the included wood screws to attach the mount to the new 2x4s.  

If this is a load bearing wall, and you're certain the studs are heavier 20-gauge load bearing studs, you might get by mounting an articulating arm using toggle bolts like these.  If the wall is non-load-bearing, it's likely made of lighter 25-gauge studs, which just don't have the localized rigidity to support this type of mount so you're stuck reinforcing with 2x4s as I described above.

If you're doing a flush (or nearly so) mount, then you can get by with toggle bolts even if you have the lighter studs.

I wouldn't recommend any kind of self-tapping screw in a load bearing application like this.  It doesn't take much overtorquing (especially with 25-ga studs) to leave them just on the verge of pulling right back out.