We did exactly the same thing - My Brit came to Ohio, we got married, he went back, I applied for a Spousal Visa and now I'm living with him in London - easy peasy.
It makes WAY more sense than anything else, especially if money is an issue (ie: paying for a fiancee visa and a spousal visa as opposed to just one). And it is honestly completely legal. It doesn't mean she gets to go "back with you" immediately, unless you apply in person or are sticking around for a few weeks and send your application straight off. As for
getting caught out at immigration or whatever when they ask what I'm vistiting for.
even that isn't an issue - and you have no reason to lie about what you are visiting for because it is LEGAL and ALLOWED!!! Once you realise that you won't need to worry. My Fiancee simply told the truth - "I'm here to get married so we can settle in the UK" and showed his return ticket home. He had a letter from his employer too, but they didn't ask for it - just let him through. In my opinion, you're much better off telling the truth then coming up with another reason for "why you're visiting" and maybe getting nervous and suspicious. That being said, you don't have to volunteer the info, just say "I'm here to see so-and-so" and if they ask to elaborate, do so.
It's OK!! What you are doing is right and everything will be fine.
PS - don't know if it applies to you, but in Franklin County you can pre-register online (fill in the licence forms) so that when you go to the court house, you skip the queue, show id, swear to not being drunk or related, give them $40 and they send you on your way. Makes it a lot quicker and easier - We got our licence and married the same day.