With the low ceiling height and 75' room dimensions, for speech reinforcement a distributed ceiling
speaker system would be very common. However, you may need a number of speakers as people's ears would be only be about 4' when seated or 3' when standing from the ceiling, thus each
speaker will
cover a somewhat limited area.
There are shallow depth ceiling speakers or you could mount recessed wall mount speakers, which are meant to fit in standard stud depths, in the ceiling, but I would verify the ceiling construction itself. A 3" depth could make it difficult to access typical
lay-in tiles so it may be something else that may be a
bit more challenging to work with. And it may not be possible to cut into the old ceiling, a common construction technique is to use a continuous layer of suspended sheetrock to help obtain the required fire separation or ratings and in those cases that barrier cannot be penetrated without whatever is done providing the same separation.
Unless you have a number of other audio sources, multiple
microphone inputs,
etc. then do you really need a mixing
console? Something like
TOA Our Products | 900 Series Mixer Amplifiers with appropriate
line level and
microphone input modules would be more common. However, a new
TOA 900 Series
Mixer/Amp with a couple of mic and
line level modules is apparently around $700 to $900, so a good portion of your budget. Luckily, you can often find used units, in some cases with some input modules, for under $100.
With the fact that nothing is existing then you may want to think about how you plan to
address local inputs like microphones and connections for a video source. Do you plan to run cables across the floor or do you install wall plates with appropriate connections and wiring back to the
mixer or
mixer/amp? A few wall plates with connectors, the related cable, any associated
conduit,
etc. may not be that much but with a $1,000 total budget it could be a factor.