This is an easy one!!
1) Two Mackie SRM450 powered speakers ($700 each, $1400 total)
These speakers have the best highs and vocal reproduction of pretty much anything out there under $1000 a speaker. They do pretty well on the lows but really should be coupled with a powered sub in the future. At a pretty low volume, these puppies will generate mids and highs that will pierce all the way to the back of your 2700 SF room.
http://www.musiciansfriend.com/srs7/g=l ... id/605255/
2) Mackie DFX12 mixer ($250).
This one has as many channels and features as you'll ever need and a good FX section for adding reverb, etc. to your vocals for karaoke.
http://www.musiciansfriend.com/srs7/g=l ... id/634264/
That is $1650 for really everything you'll need minus the wiring. The feedback problem isn't particularly going to be solved by getting a compressor and an external EQ. Having better speakers like the ones above will project your sound to the back of the room better at lower volumes, which will help a ton with the feedback and after that you should be able to eliminate the feedback with the low/mid/high EQs on each channel on the mixing board without needing all of the other stuff.
Without knowing your exact problem, I'd say you need to take the bass out of the mic channels (put them to about 9 o'clock), put the highs and mids to about 1 o'clock, and drop the bass in the overall mix whenever you are just using the PA for speaking. With the speaker/singer being in front of the main speakers, it would also help if you instructed everyone to hold the mic perpendicular to the ground instead of paralell like they normally would. The pickup pattern of the mic will take in about 30-40% less of the speaker noise at that angle.
Hope that helps!!