Over the top. It's the only way that makes sense to me. You can grab it with one hand and it rolls more easily. I can't STAND when it's coming from behind (though someone told me that's better if you have kids, because it limits how much they can roll off).
I also have a thing about toilet seats, and I don't think anyone else does!: unless in use, they should be closed ALL THE WAY! Solid cover down. I just attended an open house, and it annoyed me that the bathroom we toured had the toilet seat open. It was very clean, but I still don't want to see the inside of a toilet! There's a cover on there for a reason, and who wants their personal care products possibly falling in?