Here is a tip when drilling stainless steel. As mentioned before S/S work hardens when you work it (this includes drilling and machining) the rule of thumb is low speed high feed. This means you should select a low drill speed and apply lots of pressure to the drill.
This is a general rule which will be helpful when drilling, if you can get your hands on a drill press all the better as you can apply good pressure with the machine and hold the workpiece firmly in the vice. The risk of the drill biting in and spinning the job is greater when you are applying a greater pressure to the drill, so keep that in mind also.