Been doing safety cover for years in a Musto offshore jacket, coastal trousers and a hammar operated lifejacket.
Underneath I wear polo shirt, jeans and if its cold a fleece. Yachting wellies are good on the feet.
As some people have said you really should not need to get into the water whilst doing safety cover. (I've only had to get my crew to do it
once about 10+ years)
The downside about a drysuit is they are expensive and I find the seals uncomfortable for long term wear but dry suits alone do not keep you warm - you need the under suit.
A good hat is a sensible idea as well but that lot has seen me through hours in glourious sunshine, hail, snow, day, night and just about everything in between!