I've used wetsuits for a while, not in water detecting but for snorkeling. I'm just getting into water detecting and don't plan to change much as far as that goes. I've also used waders for hunting, and while they do have some drawbacks such as the swamping mentioned in other posts, in my opinion they have their place. Dry suits are the upper end of protection from cold and abrasions, and they're certainly the most expensive.
Neoprene waders are easier to use than a neoprene suit, faster to get into and out of, can be more affordable, and you can get different weights of neoprene with differing amounts of insulation depending on your needs. Yes, several people are drowned by them each year but thousands of people aren't. Personally I wouldn't go deeper than my upper thighs in waders, especially if I wasn't familiar with the bottom countours. Waders are somewhat easier to use than wetsuits, and at the end of the day you simply take them off and you're dry underneath. With wetsuits, not so much. Plan for either having a place to put real clothes back on for the drive home, let the suit dry, or have a good non-slip seat cover in your car.
Wetsuits also come in different weights, you'll usually find them described as 3/2mm or 5/3mm, meaning that the neoprene is thicker in the chest and thigh areas for warmth and thinner in areas like the elbows and knees for flexibility. Wetsuits are more time-consuming to put on, however wearing a lycra "thinsuit" as your first layer helps a lot in putting it on and taking it off while also adding a slight bit of insulation. You can find the thinsuits for $20-40 and prices for wetsuits can run anywhere from $80-200 or more.
You''ll get used to a wetsuit a lot faster than you think. They don't have the clunky boots built into the feet like most waders have (although you can get "stockingfoot" waders), but get the booties when you get your suit for some measure of protection for your feet and gloves for your hands. And you have plenty of options for insulation and abrasion protection. For instance in the spring you can wear a thinner wetsuit, when it gets hot in the summer you can switch to a shorty wetsuit or a thinsuit, and mix and match as fall starts to approach. A good wetsuit isn't much more expensive than premium waders, and with a wetsuit on you're ready to go after the deeper areas you shouldn't even consider when wearing waders. You can swim in a wetsuit unlike in waders, you can work the beach in a wetsuit if you want, and there's just not the bulk of waders.
Most people are VERY self-conscious about wearing a wetsuit, and a thinsuit is nothing more than a full-coverage Speedo. I can't say much without sounding offensive, but once you see some of the other people that dare to don a wetsuit you'll get over how you look. I have yet to see a woman in a wetsuit that didn't look good anyway. I wouldn't worry as much about brand names as I would the quality of the suit. It's like most other things in that you get what you pay for, the lower-priced suits have cheaper thread, looser stitching patterns and more questionable fit tolerances than a higher-priced suit of the same dimensions. Check out Neosport, Billabong, Rip Curl or Hyperflex.
I guess I could have shortened this up by simply saying "get a wetsuit", but since I'm not paying by the word I wanted to state my case. Other opinions may vary. Good luck with your decision and happy hunting!
Steve