Wireless microphone system for giving lectures I'm asking this here as opposed to a more technical stack exchange as I'm looking for a ... well... less technical type of answer. 

I'm fed up with being passed from pillar to post by my institution's A/V department when the microphone equipment in a lab breaks, and a fix that takes weeks to complete will affect my lectures (as it has done in the past). I'm consequently looking for a more permanent solution for this type of situation, one where I can take charge of my own lecturing environment and and provide some sort of recourse that doesn't involve shouting at the top of my lungs for a number of weeks.

Most of the traditional microphone systems are a complicated array of boxes and receivers. This strikes me as something straight out of the 80s and really antiquated (when we go around with small computers in our pockets, and bluetooth is a thing). It's also deeply impractical to set up, on the fly, multiple boxes that need careful calibration and separate power sources.

When I look up "bluetooth microhones" I get a whole heap of karaoke type devices. I don't know if these would work (it would be odd to receive a lecture on astrophysics that turned out to be autotuned), but even the karaoke mics that aren't covered in glitter don't look great for an academic environment.

What sort of route should I be going down? I'm in no way a technophobe, but I feel all at sea with talk about 3-Pin TQG connectors, bandwidths, stereo lines, SPL , etc.
I had the same problem.  To make me quit complaining, the department chair bought a RevoLabs USB wireless microphone.  I kept it in my office, plugged in to a USB charger wall wart, and took it to classes with me.

I'm still teaching a bit, even though I've retired, but the RevoLabs mic somehow "became lost" after I turned it in.  A new one is too pricey for me to buy at over $200, so I bought a "Fifine" USB wireless mic from Amazon.  It's neither as high quality nor as unobtrusive as the RevoLabs mic, but it's also $40 and works fine.

My use case is recording my lectures with PowerPoint; I then post a "narrated slides" video for students who missed the lecture.