Try this site to search the birth marriage and death index
https://www.1837online.com/
This site to obtain a certificate
http://www.familyrecords.gov.uk/topics/bmd.htm
Entry into america
Cyndi is well known for passenger lists (you will have to dig deep on this big website)
http://www.cyndislist.com/
And of course Ellis Island website which I have found useful (need to register)
http://www.ellisisland.org/
1901 Census online for your father is here
http://www.census.pro.gov.uk/
Did that help get you started ?