I would go according to the fees listed for application on the Home Office website.
https://www.gov.uk/government/uploads/s ... l_2014.pdf
Any other fees over and above this will vary to a very large degree by various immigration consultants etc. If you meet all the requirements, it is a fairly simple process and of course, we offer advise for free on this forum.
Your British partner would need to meet the financial requirement of £18,600pa in order for you as the foreign partner to qualify.
https://www.gov.uk/join-family-in-uk
As you are from a majority speaking English country, you don't need to meet the English A1 English requirement.
As you are in a long distance relationship, you will need to prove that you have met, communicate frequently (skype/whatsapp/bbm chat logs, emails, etc.) and any proof you have of visits or holidays etc.
If you apply for a fiance visa, the rules are largely the same, but you will be unable to work in the UK for the 6 months that the visa will be valid. You will need to get married in this time and before your fiance visa expires, you will need to switch to FLR(M) which will have another cost and will be valid for 2.5 years, at which point you will need to apply for an extension for FLR(M), which another cost involved and will be valid for another 2.5 years.
28 days before you reach the 5 years residency requirement, you will be able to apply for Indefinite Leave to Remain (ILR) at a further cost. Once you have secured ILR, you can then apply immediately for British citizenship, at another cost.
For FLR(M) and ILR, you/your spouse will need to meet the same requirements you need to meet for your initial application from the US.
As the costs for all immigration categories change on 6th April every year, it is difficult to say what the total cost for the whole process will cost, but based on what I have explained and the cost at each step, you can work it out roughly based on the current visa rates.