If you can get a mixer setup then something
along the lines of these should do for you within your budget. There are equivalents by Behringer which would be worth looking at, again within your budget. Don't forget you'll need two, and just like studio monitors, these are mostly sold as singles.
As technical advice, in this price range go for a large speaker size 12" or 15". The smaller sizes will not give you what you want and are only real any good for one-man-band pub singers and bingo callers. The bigger size will move more air without requiring large movement and thus cheaper to make. My Powered PA uses 8" drivers, but they were $1500 each... (the cabs) and I still want some subs..
An alternative (just within budget) would be a
split set like these which includes built in mixing. Again you'd need two to link together, but you save on speaker stands and a mixer... you can buy the top unit separate without the sub, but I wouldn't recommend it for the reasons I gave above.
Once you start moving into the bigger names the prices leap up to match.
Edit to add: I tried to pick examples available in US, and the prices shown are current
sale prices but are indicative of what this stuff costs.