You're right- windproof does not equal waterproof, but waterproof is (for our purposes) windproof.
And yes, there are SO many options that it quickly gets confusing. As posted, start with how much you want to spend and where you hike (Ohio?).
Main options:
Umbrellas: yes, these can work. Not ideal for the temps you are talking about, but great for light summer showers.
Ponchos: cheap, light, versatile. I only like them in summer- but even then find them a bit hot due to non-breathable fabric. I do not like them in any real wind, and you still get some moisture in and around the arms and lower legs. Not ideal (IMO) for temps below 50. Some people use them everywhere.
Non-breathable rain jackets (such as Helly Hanson Voss, Equinox's rain shells): cheap, very durable and very waterproof. However- even with good ventings options, these tend to be very hot. Often, you will find yourself soaked in perspiration. So, you are avoiding a cold soaking from rain but exchanging that for a warm, soggy soaking from the inside.
Waterproof-breathable:(everything from a Marmot Precip to Arcteryx Alpha stuff)
This is where the options get crazy. Generally, the less expensive choices use some kind of coating (each company has their own names for these) and the more expensive use a laminate (Gore-Tex, Event). These all work to some extent, with the laminates usually boasting higher breathability and durability than the coatings. This is not always true, but is a good rule of thumb.
Most people who choose a rain jacket use these as the fabrics do make a noticable differenece in internal comfort (you will sweat less). Don't think, however, that you will not sweat at all… I always do, regardless of the jacket.
Lastly, some people (myself included) carry a very light wind shell and rain shell. I do this because the wind shell (usually, depends on the shell) breathes much better than any rain jacket. Thus, I can more comfortably wear it to fend off bugs and protect from wind while remaining cool. Also, by only use my rain shell when it is actually raining, I maintain it's DWR and longevity (less abrasion, less use of zippers, etc). If you go this route, a cheap rain jacket may work well.
So, start with a budget, then what features you need (large enough to fit over a down coat). Then search the forums, most rain shells have been discussed to some degree.
If this is already common knowledge for you then I apologize, if not, I hope it helps.