Would it be best if we get legally married while she is here in the US in March or should I go over with the intention to got married when I move there?
It really depends on what is best for you.
It's much, much easier for you to marry in the US than in the UK, especially if she is visiting you anyway. She can get married on a tourist visa, as long as she will return to the UK after the wedding, and you should be able to marry within 24-48 hours.
To marry in the UK, you first have to apply for a visa that allows you to marry, then you have to be resident in the UK for 7 days before you can give notice, then you have to wait another 28 days from giving notice before you can marry... if you have a visa, your case may be referred to UK immigration, and if they decide to investigate you may have to wait 70 days before you can marry.
Marrying in the US means one less visa to apply for and you can work and qualify for the NHS right away.
Your different options:
Marry in the US- she flies to the US in March
- you get married while she is there
- you apply for a spousal visa, which costs £1,195 + £600 NHS surcharge, and is valid for 33 months
- you move to the UK, where you can work, study and use the NHS immediately
- you won't have to apply for another visa until you have been in the UK for 2.5 years.
Total visa cost to move to the UK = £1,795
Marry in the UK on a Fiance Visa- she flies to the US in March
- she returns to the UK
- you apply for a fiance visa, which costs £1,195 and is valid for 6 months
- you move to the UK and marry within the 6 months
- you cannot work or study on the fiance visa, and you will have no free NHS access, so you will need health insurance
- after the wedding, you apply to switch to FLR(M) (in-country spousal visa) which costs £811 + £500 NHS surcharge
- you cannot start working or using the NHS for free until you have the FLR(M) visa.
Total visa cost to move to the UK and get married = £1,195 + £1,311