[Apologies for cross-posting to uk.d-i-y but I was advised that there's
a wealth of
good people there even though this is an Audio question]

Our local junior ice hockey club wants to announce various messages to
the gathering masses (all three of them at most games!).
I've already plumbed my old laptop in to the Public Address system so
we can play appropriate music at the game stoppages.

So now my idea is to get a wireless radio microphone of some reasonable
quality to feed in to the microphone input of the laptop and thence on
out the headphone socket and through the PA (we need wireless because
the timekeeper's bench and the DJ area are some 50metres apart).
Plumbing through the laptop to use its mixing capabilities.

A cheap (£12) radio microphone off Ebay is no use. I've even wired up
a quarter-inch jack socket to a 3.5mm jack plug the proper way but it's
still no use.
(The "proper way" is to ignore the middle ring power connection on the
stereo 3.5mm
jack for the electret microphones commonly used with laptops. I've done
some research here, but am willing to admit my fallibility).

I'm looking for advice:
Anyone done this before?
What impedance microphone should I look for?
Any good sources for the kit?

The club have a budget up to (I guess) £100 but cannot afford much
more for anything
sophisticated.

Any help appreciated; thanks in advance

Mungo