I don't think there's any difference who files first, but from what you've described it sounds like you are ready for it, and I think by filing first it will help you feel even better about yourself. There's power to it. It's forcing the whole situation off the fence.
I agree with Cat about being a nice person and letting him know that you've done this. I've always found there's nothing to be gained in doing things that may be perceived as mean, but much more to be gained in kindness.
I would probably even present it as something I was doing for my husband. That I wanted him to be happy and giving him the freedom to move on in his life (even though I'd be doing it for me too!).
Good luck to you.
There is no arriving, ever. It is all a continual becoming.