What type of gun is primarily used by the protagonist in "Blue Ruin"?

It's specifically described in the movie by his friend as a Ruger Mini 14, not an M14. It also referenced the stainless Mini 14 from A-Team.

This appears to be an M14 used by the US Military 1959–1964 and is still in service by other countries:

The weapon used in the top picture above moving through the woods) is in fact an M1A which is the Springfield Armory civilian version of the military M14 (7.62 caliber). The M1A is semi-automatic. The M14 is capable of fully automatic firing, therefore it is considered a machine gun.

The rifle in the second picture is a Ruger Mini 14 (.223 caliber) semi-automatic rifle. One does not have to look very closely to see the dramatic different between the two rifles. When the protagonist is given the rifle by his high school friend, he is told that the magazine holds 20 rounds. This is not correct. The magazine pictured in the movie is a 30 round magazine.

The last gun Dwight is given by his friend Ben looks to be a Taurus/Rossi "Circuit Judge" revolving Carbine/Shotgun.

The carbine shoots both .45 cartridges and .410 shot-shells/slugs. Ben's Circuit Judge appears to be a slightly rarer combination of black-oxide steel and wood furniture.

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Wikipedia page on both pistol & carbine models: https://en.wikipedia.org/wiki/Taurus_Judge