If I had to start over with that budget, I'd get a Line 6 L3T or L3M with a small format mixer. Most of my smaller gigs are that setup. The "T" model has a built in 2 channel mixer with sweepable mids, but I like having the mixer on my left hand side, and I don't want to have to be right next to the speaker for adjustments. Otherwise, I could be just fine with just the L3T.
Bigger gigs get a subwoofer and crossover, but I loop beats and basslines through a Boomerang III. Most people don't need all that.
The Line 6 speakers kicked my QSC K10's to the curb. They sound noticeably better.
Chill low volume patio gig (no sub or crossover)
Another no subwoofer patio gig
Most of the full rig for comparison:
