Mixers are the brain of the PA system. A forty-dollar mixer can work but at the same time people get what you pay for. The professional mixers I recommend is the Yamaha MG06X and his bigger brother Yamaha MG10XU.
The MG06X is the size of an ipad. You can connect multiple microphones to it and have so much control of the gain, highs and lows. Also it has buttons to mute out a microphone if needed. A 2 dj setup can be connected with this mixer. The beauty of this mixer is it can be added with another music system and it gives you more headroom to add more volume if needed. Each channel has a gain and then the master gain can be increased. If a dj decides to just play music and use microphones off his dj set up it sounds a certain way. Most controllers do not focus on the clarity of the microphones. They have other attributes it focuses on. But if the microphones are connected to the Yamaha mixer, it is so much clearer and it gives the option of multiple microphones. The mixer can be purchased for 120 dollars.
The older brother Yamaha MG10XU is a force of nature. Four microphones can be connected with the mixer. The highs, lows, and mids can be manipulated plus it has 24 effect programs that can add to the channel such as delay, flanger and echo. This mixer is so much bigger than his little brother so you would need more space for it. This mixer can be purchased for about 200 dollars.
Both can do the job and it depends on how many microphones are needed and how fancy somebody wants the effect to be.