Getting married in the US does not require a visa if you don't intend to make it your permanent residence. There are minimal residency requirement to marry in the US. If you marry in the US you have to apply for the spouse visa from the US and once it is issued you can travel to the UK. If you go this route, you can work as soon as you arrive in the UK with your spouse visa. One visa, one fee. In the long run, you will need an additional FLR in 2.5 years and then ILR after a total of 5 years and citizenship if you want it but it's not mandatory. So, 2 visas plus ILR, 3 fees. Citizenship is optional plus an extra fee.
If you want to marry in the UK then you must first apply for a fiance visa from the US. Once that is granted and you arrive in the UK you will have 6 months to marry during which time you cannot work. Once married, you apply for FLR and once granted you can work. As I have already stated if you apply for FLR by post you can wait months, with an in person appointment the visa is usually issued same day. Two visas, two fees plus and extra fee is you go for an in person appointment. Again, in the long run you will need an additional FLR in 2.5 years and then ILR after a total of 5 years and citizenship if you want it but it's not mandatory. So, 3 visas plus ILR, 4 fees.Citizenship is optional plus an extra fee.