What is safer...coaster brakes, rim brakes, or fixed gear braking?
A track bike (fixed gear) has no front or rear brakes.  You slow the bike down by resisting the turn of the pedals but you need to be careful to not push too hard, which can lock up the rear wheel and cause a skid.

But most fixed gears aren't true track bikes.  You should be able to find one that has standard brakes on both the front and rear wheels.  The front brake is especially important since that's where most of your braking power comes from on a normal bike.

A coaster brake is basically a drum brake in the rear hub.  Pedalling backwards engages the brake.

Personally I would expect a bike with a normal front rim or disc brake to be "safest".  Front brakes have much more stopping power because your weight shifts to the front wheel when slowing down.  Plus you can control the amount of braking power more easily by hand than by resisting with your feet.