The challenge with a gymnasium is first and foremost acoustics. As the first poster said it’s less about speaker size and more about how the speaker pattern sends acoustic energy into the space. To combat this, many highly reverberant spaces use steerable line arrays that focus sound energy at audience members in a narrow beam, thus reducing the amount of sound energy and early reflections.

That said, a good steerable line array will run over $2K, easily, before mixing and amplification. So thats not an option.

It’s great you’re asking the right questions but honestly for $300 you’re not gonna find anything that’s going to address the reverberation or the amount of amplitude you‘d need. A friend has a warehouse similar size to a gymnasium and uses a Fender Passport PA. When the space is full of people it’s impossible to hear.

The knockoff brands will have to suffice unless you get more funding. If you do end up getting more money the I’d at minimum go with a QSC K10.2 Active 10" Powered 2000 Watt Loudspeaker https://www.amazon.com/dp/B06Y4BT184/ref=cm_sw_r_cp_api_i_30zEDb9GTBB5N