For that budget, you can get proper, pro level kit. (Are we talking USD here? I’m never sure when people just use a $ sign – this is a multinational forum… 🙂 )
I would recommend (whatever you get) getting subs and tops from the same brand though – often they are all designed to work together. You are right that 2 12″ tops and an 18″ sub will probably be your best bet.
Possible options:
Mackie SRM 550/1850 setup. Rough cost: $2100 USD
QSC KW122/KW181 Setup. Rough cost: $3600 USD (A little over budget..)
QSC K12/KW181 Setup Rough cost: $3000 USD
Yamaha DSR112/DSR118W Setup. Rough cost: $2800 USD
JBL PRX712/PRX718XLF Setup. Rough cost: $2900
Any of these will sound decent – I recommend you go to a decent shop and have a listen to as many alternatives as you can. Sound is a very personal thing though – some people prefer the way that JBL sound, some people prefer QSC. It’s entirely subjective and I recommend you listen to them properly in person.
bob6397