The best source possible is a book written by Dick Lamb and Bert McGrane called "75 Years with the Fighting Hawkeyes". It covers 1888-1963 and really provides everything you would ever want to know about those years.
Some tidbits:
Iowa won Big Ten titles in 1900, 21, 22, 56, 58 and 60.
The team also finished in the Top 10 in 1939 and 1953.
Iowa won a National Championship in 1958, as recognized by College Football Data Warehouse (a great source for football history).
Old Iowa Field sat about 28000 and was located at the current site of the English Philosophy building.
Kinnick Stadium hosted its first game in 1928.
The 1953 tied undefeated, #1 Notre Dame in South Bend in the infamous "fainting game" (Evashevski, our coach, forever after called them the Fainting Irish and absolutely slaughtered them in 56, 57, 58 and 60!).
Alden Knipe, the coach of the 1900 Big Ten Champs, was a famous Opera singer and retired from coaching to write children's books (he was very successful).