This is a quick pic of a typical Wednesday night tech setup. The computer is connected via an HDMI cable to a TV. We use the laptop/TV combo to display the text to the songs we are singing.
Beside the computer is a small audio mixer. There are two mics connected to the mixer. One is for me, and the other is for my vocal assistant. The computer has an audio output that runs into the mixer. I also use an iPad loaded with any tracks that we might be singing, and the audio from the iPad feeds into the audio mixer as well. I do not mic my guitar since our room is small enough that it projects fine without application.
The audio mixer is connected via two microphone cables to two powered speakers sitting under the TV which is on a cart. (Although the picture is not very clear, you can see these black speakers on the bottom shelf next to the stacked books.) These are pretty small speakers, but they work well for our setup. The room we assemble in gets utilized for many other things throughout the week, so any equipment we use has to be easily transportable. I keep everything in a small tub. It takes me about 20 minutes to set all this up each week.