All sizes and types of fixings are dependant upon the size and weightof the object to be fixed, and the type of material it is being fixed to.
Bricks are great for fixing stuff to as they can take quite a heavy load.
You will need suitably sized screws to hold the object, a masonary drill bit (usually silver in appearance) and some rawl plugs (trade name I know but everyone here knows what they are!) Visit your DIY store and they will help you out with sizes as the rawl plugs (thats the plastic insert that goes into the drill hole and gives the screw something to grip onto) need specific sized holes to be drilled in width as well as depth.
If you just wanted advice on particular screws to use then the non-rust variety would be ideal for outdoor use.