Welcome to the forum and good luck with your plans

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As you mentioned talking about the steps for getting a fiance visa, I'm assuming you are just a visitor in the UK at the moment, and have a 6-month visitor stamp in your passport?
If so, then the most important thing is to make sure you leave the UK and go back to the US before your 6 months is up (presumably this will be in December sometime, if you entered in June?). You can't switch to any other type of visa from inside the UK while you are just a visitor, and if you don't leave the UK before your 6 months is up, you will become an illegal overstayer.
If you will be getting a fiance visa, you will need to apply for it from the US and then move to the UK after you have it.
Alternatively, if you have time before you have to leave in December, you could technically get married while you are in the UK now as a visitor (in theory there is nothing preventing you from marrying here as a visitor) and then you would apply for a spousal visa in the US instead of a fiance visa (which would allow you to work immediately in the UK, while you cannot work on a fiance visa). To marry here, you would need to give notice to marry, and then wait a minimum of 15 days before you could have the ceremony.
In DESPERATE need of some delicious mozzarella sticks with ranch and marinara, FLAMING HOT CHEETOS, sour patch kids (American style)
Speaking of Sour Patch Kids, I just noticed that Maynards are now producing them in the UK - anyone tried them? I was wondering how they compared to the US version.