The first step is to figure out the kind of venue that you will be playing, because you can potentially save yourself a lot of money by matching your equipment to the venue. For example, if you're going to be playing in clubs that host a lot of live bands, chances are these places have their own permanent gear: A PA system, speakers and a house mixer permanently installed. This is the best-case scenario, because all you have to do is hook into that system. In a club with this kind of equipment, grab your instruments and a couple of microphones and you're ready to go. If that leaves you feeling a little empty handed, you could bring along your own mixer -- it's not necessary, but you'll have more control over the sound.
If you are playing in theaters and/or school gyms, the same is true -- there may already be equipment on hand, and you don't have to bring anything besides your basic gear.
But, if you are going to be playing at parties, or in clubs and school gyms that don't have equipment, then you need to have your own setup in tow.