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Most anything will work right up until it doesn't.
Had a relative that "claimed" he had to stop his car for a deer in the road, He got out with a High Standard .22 pistol and when the deer didn't move he fired one round at the deer. the Deer fell over, He said he about fell over too, in surprise. He hit in the head, He wasn't aiming at the head.
I have also chased all over a Vermont mountain after a deer leaking blood from multiple buckshot wounds from another "hunter" in our party (never trust anyone who empties his gun every time he even glimpses a deer) When we finally found it (and finished it off) it had been running on 3 legs as one of it's legs had been broken by one of the multiple hits.
Use enough gun to make up for minor errors and go to the range enough to make sure your errors are minor.
Mossberg 500 or Remington 870 in 20 Ga, both well under $300 at your local Wal-Mart.I also hope to get an inexpensive 20 gauge pump before the next duck season.