Should I do Msci or Bsc + Msc , if I want a phd in us ?

If I am studying in Uk , I can chose to do either a 3 year Bsc or a Msci (which is 4 years , 5 at edinburgh) in geophysics .
If I do the Msci then will I be able to do my phd in us ? , or do I have to do the master again in us ?
If I chose the Bsc can I do my master+phd in us ?
If I do the Bsc+Msc in Uk , can I do my phd (without doing the master again) in Us ?

Out of these options , which would be the best ? Also , I wouldn’t want to repeat the master and I doubt that the Msci (which takes only 4 or 5 years!!) would be enough to go for a phd in Us .

Usually if you already have an MS, you won’t need to complete a second one.