Peavey has been building road worthy equipment for decades. Mostly powered mixers for small and medium size bands. Their stuff is not high end but it always gets the job done and lasts forever.
Carvin is another name that's been around forever and they make decent live equipment as well. Very well built and sounds decent at an affordable cost.
TASCAM, while not known for live sound re-inforcement made many affordable recording consoles that can double for live sound. Pretty darn cheap right now too as most are recording digitally and the market is flooded with analog consoles. The builds are a little lighter as they were not made for gigging, but if it's not going to see any road use, these consoles might be your best value. They are unpowered though, so you'll need an amp.
A suggestion would be what I currently use, the M-1516. A sixteen channel desk, three sends for monitor mixes as well as several other outs. Cheap too, but you'll still need an amp. Typically anywhere from $50 to $150 on e-Bay. Make sure it comes with the power supply.
I would avoid Berhinger for live sound. No matter how cheap it is, you get what you pay for. And with them, that's not much.
I don't know what you want to drop on a live sound desk, but for new, Yamaha and Mackie both make affordable live sound desks. So does Soundcraft.
Turner Model 1 C-LB, Seagull S6+, Ibanez 12 string, Dean Bavarian Vendetta
VOX AC50 CP2, Roland RE-20, Boss CE5
Kurzweil SP88X, Yamaha MM8, Roland R-5
TASCAM 38-8, Behringer SX4882, Alesis Midiverb III, Alesis Midiverb IV, DBX 262, DBX 266, Omnifex DDX1024, TASCAM DBX Type II NR
Sennheiser MD441, Shure SM57, SM7, Sennheiser 402's