Looking for Jozwiak family history

Looking for lost family. My grandfather came from Poland. Don't know what part. His name is Joseph (Jozef Jozwiak) born 1877 in Poland. Died 1952 Gaylord Michigan. His father was Valentine Jozwiak. Married Malgorata Oliporkak.
Joseph Jozwiak married Leocadice (leocadya) Veinecka Her mother's name was Gorit Kriow. I have no idea what region they came from or what part of the United states my grandpa ended up at. History seems to start with the marrage in Gaylord Michigan. (nothern part of Michigan) Any help would be appreciated.

Number by variation in Poland (2002 census) Jozwiak (10), Jożwiak (3), Jóżwiak (93), Joźwiak (9) (www.moikrewni.pl/mapa)

Lower than I anticipated. Am I missing a variation?

Determine which variation is the ancestral spelling and it'll be a little easier to determine potential living relatives. But immigration records should have home town available.
Did Joseph come over by boat. Records may be available.

There are nearly 20,000 people in Poland named Jóźwiak. It is the ź with the acute accent over it, not the dotted one: ż.

Since there are 20,000 Jóźwiaks in Poland, scattered acorss the country, you would have to have at least a rough idea what part of the country or (if prior to 1918) which partiton zone they came from. Otherwise even the best genealogist will have nothing to go on. Any old, yellowed envelopes with Old Country return addresses, vital documents, etc. lying about?