Question about Marriage on Partner Visa

I have what may be a stupid question about being able to get married on an unmarried partner visa:

If we were to go through with it, would we have to do a Fiance Visa, then do another visa, or would we just apply under the same circumstances next visa renewal, with the only difference being that we're now married? Just want to make sure before we do anything, I'm already in the UK on the partner visa.

Thanks for all the help!

It changes nothing, it's just that you are now married versus unmarried partners.  The next visa application, you'll state that you are now married.  The clock to Indefinite Leave to Remain will still be the same date as when you started on your current path. 

Congratulations!