You're best off with trail/fell shoes as they have better grip and it's good to have shoes that release water quickly. Me and the Other Half have Innov 8 (£80 - £100) and they've been good. Only thing is like you I'm an overpronator and I have yet to find any grippy shoes that are as supportive as my running shoes. My sports therapist has recommend seeing a podiatrist to get inserts.
Kit - best to wear clothes that dry quick and don't fall down under weight of water. I think sleeves are essential after rubbing my underarms raw going over A-Frames. A lot of people wear as little as possible - vests and shorts. Also gloves can be helpful to give you grip when you hauling yourself over the obstacles.
I'm just looking at it as well. Already done the 10k X Runner versions and it does look epic. I'm going to enter the 20 miler (as it all costs the same) and hope to do the 13 miles.
It definitely looks great and at £119 for the weekend v £75 for Tough Mudder it looks a bargain.