You asked about steps to take, and my advice would be:
- Spend the next few months communicating over the phone/email/messages, and save your call/message logs
- Visit each other when you can in that time and spend some time together to really get to know each other. If she hasn't visited the UK before, she'll want to see if she actually likes the UK. Also, living in a new country can be very different to just visiting, so she would need to make sure she could be happy here.
- start thinking about whether you seriously want to get married and settle in the UK together.
- start looking into the visa application process
Marrying in the UK
- if you decide to marry in the UK, she would need to apply for a 6-month fiance visa, to marry within those 6 months
- the fiance visa currently costs £1,464
- she would not be allowed to work or study or use the NHS for free (so she would need health insurance or she will be charged 150% of the bill for treatment)
- you marry in the UK within the 6 months and then apply for an FLR(M) visa extension for her to stay
- the FLR(M) costs £993 + £500 IHS surcharge (which allows her to use the NHS for 'free')
- once she has the 30-month FLR(M), she can work, study and use the NHS for free
- she will need to apply for a second 30-month FLR(M) just before the first one expires
- after 5 years on FLR(M), she can apply for ILR (permanent residence)
Marrying in the US
- you fly to the US and get married
- she applies for a 33-month spousal visa to move to the UK
- the spousal visa costs £1,464 + £600 IHS surcharge
- once she has the visa, she can work, study and use the NHS immediately
- after 30 months in the UK, she applies for FLR(M)
- after 5 years in the UK, she can apply for ILR
Also, the costs of visas keep rising, so you would need to budget approximately £10,000 in visa fees over the next 5/6 years.
Current prices:
Fiance visa: £1,464 (plus £551 for priority processing if you choose to use it)
Spousal visa: £2,064 (plus £551 for priority processing if you choose to use it)
FLR(M) visa: £1,493 (plus £590 for an in-person, same-day decision)
ILR: £2,297 (plus £590 for an in-person, same-day decision)
UK citizenship after gaining ILR: £1,282
However, the visa prices rise every March/April and they are currently approved to rise to a maximum of £3,250 by 2020, but they could go higher after that.