Tim,
Yes, that style of starter and solenoid both were used starting in 1957 on passenger cars 6 and 8 cyl. The trucks maintained the old "lever" style of starter with the small push button switch on it. The exception to that was if you had an automatic transmission and V8. That starter would have had the same solenoid but different starter than what is pictured.
1961 is the first year for the starter pictured to be used on Chevy 6 cyl. trucks. Delco #1107888
So it either has to be a 57 or later car motor or a 61 or later truck motor. My above posting said after 61, I was going off of memory and looked it up so Im correcting myself now.
If the starter is original, which it looks to be, there will be 7 numbers and a date code stamped into the starter case. If I had those numbers I could tell you the year of the starter and what it could have been on. If its original that will also tell you the year and application of the motor itself.
Ken
