If you're serious about the audio video flexibillity, lookout for camcorders that support mic/line in. You have a few options with that jack:
1. Direct in/wireless transmitted from the PA system.
2. XLR adapter with 2 channels, one channel direct in/wireless and the other channel external mic. You can do alot of an XLR adapter.

Most of Sony comcorders has audio/mic in, which u can used for audio in recording with the PA.
But last time my experiment using standalone video+PA audio mix soundtrack given a quite good sound. The audio from camcorders give an ambiance while PA sound gives a base audio. So mix it together (Cam 30%+PA 100%) the audio seems like surround sound..

If budget's not a problem, then you might want to look at video cameras at the prosumer range which gives you the option to enable/disable gain control and volume control for each channel. Standard def would start around RM8k (Panasonic DVX, price has probably dropped) or High Def starts from RM10k. Panasonics and Canons prosumers cams all have XLR input (as well as phantom power support). Not all Sony models include XLR support.

Regardless of the reliability of wireless signal for convenience or cabled application if you're anal, you should always have a sound recorder as secondary recording to put you on the safe side.

If it was a consumer camcorder, you have to make sure that the camera has features to disable automatic gain and the ability to control the audio level (Most, maybe all consumer cams which have these features can't control the volume for each channel separately). A two channel XLR adapter is good enough if the camcorder is able to just turn off the automatic gain control. XLR adapters would have knobs for it's own volume control. So one for line in, and the other external mic. However, remember that XLR only carries one signal per channel. So if you want STEREO sound + ambient sound, that'll be

3 channels = Stereo PA + Mono Ambient
4 channels = Stereo PA + Stereo Ambient

It was 3/4 channels synced into one camera, you might want to check out the Panasonic HVX.

I'm guessing most Canon and Panasonic consumer cams have these 2 important audio features at their upper range. A Canon HV20/HV30/HV40 has these, they may be taped based cameras but a friendlier HDV codec to work with compared to AVCHD. And still there are other brand options of other newer cameras than the Canon HV series.

There's no problem with wireless, it's just prone to inteference. It might not happen, but if it does, just make sure you have a secondary recording going on just in case if anything goes wrong. Try look at Sennheiser's range.

I just remembered there's another camera model with 4 audio channel recording; the Panasonic HPX (RM16k, records to P2 cards), cheaper than the HVX (RM20K, records to P2, miniDV). If 2 channel recording is fine, there's the HMC at RM13k (records to SD cards).

Then you have the consumer series, Canon's HFS series or Panasonic's TM or HS series. Remember to test the features you need before buying them. Followed by a 2 channel XLR adapter, make your choice if you need phantom power.

The cheapest option would be, RCA to stereo line if you don't mind ambient and music both mono. Since you have a PA system, volume of each channel output controlled. And a wireless transmitter can be thrown into the mix. All the best!