What I am trying to setup is a single microphone that can be used by a presentation/classroom type person to a small room approximately 15x30feet

the caveats are:

1. the environment sometimes gets very very very heavy rain and the main use of the system would be to amplify the voice over the ambient noise to those in the corners or sitting just outside the room

2. system must be entirely battery-powered and wireless

some questions I Have are ... 1) how necessary is it to stay away from lavalier mics? an old setup used a very cheap lavalier mic and worked ... OK. I understand they are worse for picking up ambient noise but also this is not a symphony orchestra we are just trying to make words be audible/intelligible to a small group

2) is there any issue at all with latency using bluetooth like this for spoken words / presentor?

also the group already has access to several standard JBL type cylindrical bluetooth speakers, so bonus points if those could be used for the interface. also not necessary but might be nice if expandable to use 2 or 3 speakers in various parts of the room.

thanks for any thoughts even if doesn't satisfy whole criteria. main questions are on latency and mic type if those are actual issues or if it will be okay for spoken words.