Well, here's a subject I can chime in on.
I've been using wireless headset mics for over 20 years. I've got experience with different styles from many manufacturers. I use wireless headsets because both my hands must to be free to play my instruments. To keep it easy, I'd go for a wired headset and you won't run into other signals breaking into your announcements.
For general P.A. announcements, try to get a
dynamic instead of a condensor microphone. Dynamic mics are better for general announcements, they'll cut through better than a condensor. Condensors would be better for singing or recording.
Clip on or Lavelier mics sometimes require a hotter signal because the mic is farther away from the mouth. More gain, more chance for feedback. Some Lav mics are omnidirectional, taking sound in from all sides. You are best off with a unidirectional mic. Be sure and set the speakers in front of and away from your microphone.
If you want to go wireless, go to the Audio Technica website for great general information.
These two pages may answer some questions:
https://www.audio-technica.com/cms/site/2b1098a99bf0f43b/index.html
https://www.audio-technica.com/cms/site/af9d127e26abf498/index.html
Hope this helps!