if you're running in the rain you are going to get wet so there's little to gain by going over the top. Which is why running waterproofs tend to be much less elaborate than walking ones... The trick is keeping you reasonably warm by keeping most of the cold water out.
I'd just go down to your friendly neighbourhood running emporium and see what they've got and what you find comfortable.
Showerproof is generally nicer for running in than waterproof as it'll be a lot less sweaty, all else being equal. The problem comes on longer runs where you'll more likely start getting cold in a showerproof as once the rain has soaked it through you'll be getting lots of cold water in. if you'll only be out for half an hour that's not so much of an issue though.
Pete.