You're lucky; there are quite a few brands of gear now that work for GUE-style diving. I dive, and have dived since before Fundies, a Deep Sea Supply horseshoe singles wing (35 pounds, I think) and a steel plate. DSS setups are nice for singles, because you can add weight plates to the plate itself, to minimize the weight-belt or harness ballast you need to carry in cold water.
The difference between cold and warm water setups is related to ballast, and how that affects required lift. In cold water, using a steel plate makes sense, because you have to carry so much weight to sink, anyway. In warm water, where the weighting needs are minimal, one might end up overweighted with a steel plate and no other weight at all! And if you don't have much buoyancy to lose, you don't need as much lift, so a smaller wing can be used. But it isn't critical; I dove my singles rig in cold and warm water until I ended up with one of DSS's 17 pound wings, and now that I dive dry everywhere, I tend to dive the bigger wing again.
Any good regulator will do. There used to be a proscription against Poseidons, because they were upstream regs, but they're pretty rare nowadays and I believe they no longer make the upstream models, anyway. It is preferred to have a reg where the user can remove the face plate if necessary. But you can read about all that on the GUE website -- there's a good article about equipment there.
Paddle fins with spring straps are ideal. Lots of different fins are used, although Jets are probably most common. But to get a good foot pocket fit, people also use Hollis fins. If you like neutral fins, Dive Rite makes a good paddle fin that comes with springs. My personal favorite are the Mares Power Planas, which also come with an elastic strap.
Backplate and wing, long hose, paddle fins, wrist computer/depth gauge -- that's about all you need for initial training. A strong, focused light would probably be the next addition.
