Lot of credit to @Stiv for this who got the final answer when I was turning down a large rabbit hole (see edits for a laugh).
Logic at the bottom for the starting point, though I think it was almost impossible before the hints.
These are all relating to:
The song lyrics for Heartaches By The Number, specifically the last word in each line (assuming you're not looking at a version that combines pairs of lines)
20 (compared to 350)
20 (compared to 3)
20 (when scored by the NY Giants in 1991)
Win (this really threw me - knowing nothing about American Football, googling it showed me the Giants had a mediocre 1991 season after winning the previous Super Bowl. Didn't realise it had been in January
20 (when the last in this list)
Logic for identifying the connection:
Dude found in part of GUam? WhY? (3) => GUY
MST3K movie has Chet troubled in mill (8) => MITCHELL (only possible anagram of chet inside mill, plus on a list of MST3K movies)
So that gives us
Guy Mitchell, for which the only reference I can see is [this singer]. Can't see how any of his songs listed are relevant to the clues though3.
However, having now solved Hint #1
Result of rifle placed by oaf (7) => FALLOUT (FAL + LOUT)
It turns out that:
Heartaches By the Number was a Guy Mitchell song featured in Fallout: New Vegas. So presumably all the clues refer either to the game, or to heartaches, or troubles
The second half of the first line of Heartaches By the Number is "...troubles by the score". 20 = a score, title is literally "troubles" by(beside) a score