Hello Mark
To find an ancestor in Canada in your time period you will need to narrow your location to a province at least -- do you have any clue what province they might have settled in?
For example, if it is Ontario, then you can consult the Vital Stats index either on microfilm (Ontario Archives has it, so does Library & Archives Canada) or take a peek at the OSVR project online. They don't have it all indexed but it's a place to look at least. However, births are only public from 1869-1908. See
http://www.archives.gov.on.ca/english/interloan/vsmain.htm You can order (and pay) for searches of later years from the Office of the Registrar General. See
http://www.cbs.gov.on.ca/mcbs/english/welcome.htmBritish Columbia has their vital stats indexes online at
http://www.bcarchives.gov.bc.ca/textual/governmt/vstats/v_events.htm but births are only 1872 to 1903
You mentioned the 1911 census - there are several projects underway to index it, so you might want to check those sites to see if by chance your family is there.
Try
http://automatedgenealogy.com and
http://allcensusrecords.com/canada/ Both are indexing/transcribing 1911 for all of Canada so you really should have a look.
Ontario GenWeb Census Project is indexing/transcribing 1911 just for Ontario if that's any help.
Regarding immigration records, for 1902-1915 you are in for a long search if you want to find their names on passenger lists. Unfortunately the records before 1925 are not indexed. To
find a passenger you will need to know an exact date of arrival.
The National Archives of Canada (NAC) holds immigration records from 1865 to 1935. There is no easy way to search Canadian arrival records for this unindexed period other than reading microfilm. . You can find the details at this URL
http://www.archives.ca/02/020202_e.htmlIf you want to order filmed passenger lists (remember they aren't indexed!), a list of NAC microfilm numbers for passenger lists to Canada 1865-1922 can be found at
http://olivetreegenealogy.com/ships/filmnos_can1865.shtmlIf you want to try your luck searching transcribed ships passenger lists online, passenger lists for Ships to Canada after 1865 are freely available at
http://olivetreegenealogy.com/ships/tocanp05.shtmlYou can also try TheShipsList.com at
http://www.theshipslist.com/ They have been indexing
arrivals from Newspapers and have many passenger lists online
But there are not many transcribed for Canada so it's a shot in the dark