So then it is possible to go over there as a tourist and decide to apply for a marriage visa during that visit? I mean, I wouldn't have to have some sort of visa (fiance, student, or whatever else) when I first went over there?
Yes, you WILL have to have some sort of visa to enter the UK. If you get married in the US, you will need to go to the British Consulate *in the US* to get your spousal visa. You're then able to legally enter the UK to settle, and can work immediately once you get here.
What kind of proof do you have to have that you have the funds to support yourself? - a bank statement I'm assuming. And how much is enough - I won't be having to pay rent or anything cuz I'll be staying with him.
For both the Fiance and Spousal visas, you'll both need to show three months worth of bank statements, letters from employers (probably just his since you won't have a job in the UK yet, I assume). You'll also need some proof that you'll have sufficient housing, like a lease or mortgage papers.
There is no set amount for how much you need. But you should be able to show that you are able to support yourselves without the aid of public funds. So if you have a good employment history or a CV/resume that shows you are employable, or if your partner makes enough to support you both fairly easily, that will be good.
Best to check out the IND website for the details, but I hope this helps a bit.
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