My wife applied through the embassy in DC, and it took just a couple of days (back in 2000), but I think that the consulate in New York has a fast-track same day service.
The visa is initially good for a year, which can then be made permanent after a year, assuming that you are (i) still married and (ii) still living in the UK.
It is entirely up to you as to whether you ever want to "upgrade" to British citizenship though, there is no compulsion to do so, but there are some benefits, like voting in elections, and scooting through European airports without being given the third degree!