Let's see if I understand. The performance is a DJ, no band. You would be renting the
system and the company providing the
system would be running it. Room is a typical gym and about 50' x 100', not sure if the DJ will be at an end or side of the room, and they'll be spinning hip-hop. The budget is "as low as it needs to be".
Does that budget description mean that if someone says it will take X dollars then you will come up with that amount regardless of what it is? Or does it mean that you want to keep it as low as possible but there is some amount that you can't exceed? Have you never had a dance there before that might provide some idea of what it takes or costs?
My first thought is that most DJs provide their own sound and lighting systems. Even if they have to rent them because it is a larger event for them that puts the control and responsibility for the overall show in their hands rather than splitting it between multiple parties if you have someone else provide the sound and lighting systems and operate them. It would not be unusual to have disagreements regarding the sound levels and quality, if I am providing the sound then I'm not going to risk damaging my equipment or my reputation for providing my perception of quality sound while the DJ may feel the same, yet the two perceptions of what is 'right' may be at odds with one another. For example, if the
system is being run as hard as I am comfortable with, then I'm not going to turn it up regardless of what the DJ wants.
If you rent then what you are going to be able to rent is probably going to be limited to what is available from local providers and your budget. If we try to get into specific equipment then the chances of what would be recommend here actually being available locally or matching what a local provider proposes is small. It might be better to talk to a couple of possible vendors, explain the situation as thoroughly as possible and get their proposals, then we can comment on those if desired.
One specific thought, have you considered creating a dance area rather than trying to
cover the entire space? I find that people sometimes like the idea of having some areas with lower levels where they can more easily talk or simply rest their ears a
bit. Think about if you really think you need to
cover the entire space with high levels or if it might be better to focus on a smaller area right in front of the DJ.