Welcome to Just Answer and thanks for your question. Do you know his wife's name? Where he came from?
Thanks for the additional information. I spent about 3-4 hours on this and below is all I could find. He says in several places that he came to the USA in 1901 but I can't find an immigration record for him. As of the 1930 Census, he was still not a naturalized US citizen. He also mentions in 1917 that he is supporting his mother but I can find no evidence of her either.
1930 CENSUS - Randolph Twp., Morris Co., NJ, District 64, Enumeration District 19
Hugo Rost 40 M Head b Germany both parent b Germany came to USA in 1901 Occupation house painter
Stella 41 F Wife b NJ both parents b NJ
Walter 13 M Son b NJ father b Germany mother b NJ
Edna 12 F Dau b NJ father b Germany mother b NJ
Earl 9 M Son b NJ father b Germany mother b NJ
Pauline 7 F Dau b NJ father b Germany mother b NJ
1910 CENSUS - Randolph Twp., Morris Co., NJ District 0040 Enumeration District 5
Fred Crater 38 M Head
May 38 F Wife
Russell 17 M Son
Edna 13 F Dau
Earl 10 M Son
Beatrice 3 F Dau
Hugo ROST 24 M BOARDER b Germany both parents b Germany came to USA 1901 occupation laborer in stove works
1910 CENSUS - Randolph Twp., Morris Co., NJ District 0040 Enumeration District 8
XXXXX XXXXX 55 F Head b NJ both parents b NJ
Stella M MOORE 20 F Day b NJ both parents b NJ
These 1910 Censuses confirm that Hugo and Stella didn't marry until sometime between the summer of 1910 when the censuses were taken and the birth of oldest son Walter about 1912/3/4. I have no doubt they were in Morris Co., NJ in 1920 (see the 1917 Draft registration below), but evidently the census taker missed them.
WWI Draft Registration Card dated 05 June 1917
Born 12 June 1887 in Germany (town looks something like "Steten")
Citizen of Germany
Self employed farmer in Millbrook, NJ
Support wife, 3 children, and mother (Evidently there was another child besides Walter b abt 1912-4 and Edna b abt 1917.) This is where that 1920 census would be so handy.
1900 CENSUS - Randolph Twp., Morris Co., NJ District 76 Enumeration District 19
XXXXX XXXXX Head b May 1845 55 M
Anna Wife b Oct 1854 45 F
George Son b Jul 1878 22 M
Charles Son b Jul 1884 16 M
Fred Son b Mar 1856 14 M
Stella MOORE Dau b Jul 1890 9 F
Price Brother b Jul 1847 52 M All b NJ, all parents b NJ
Stella Moore Rost - Social Security Death Index
B 11 Jul 1889 d Aug 1964
Daughter of XXXXX XXXXX and Anna of Morris Co., NJ.
Thanks for the accept and the lovely bonus. You can probably make copies of the censuses off the microfilm at your nearest large library with a genealogy department. If they don't have the filmed census images (most will) they can order them through inter-library loan. They will probably have the WWI registration microfilm as well, or they can get it.
For birth, marriage and death you will need to deal with the New Jersey Department of Vital Statistics, and they don't make that easy! To get copies of records, you need to tell them lots of detail down to the date something happened. Without an exact date it will take months for them to search. Both NJ and NY do that and I have had to wait as much as 9-12 months to get the papers I had ordered. Good luck!