Very nice finds....
Actually, the silver military item you found is not a "Marksman" item, but an "Expert".
There were three possible grades of pin you could get according to how well you did on the rifle range during basic training in the Army.
The three grades were "Marksman", the lowest grade, then "Sharpshooter", and finally "Expert". The three pins were similar in design but with a small difference for each grade. The Marksman pin was just the cross, the Sharpshooter was the cross with the bullseye, and the expert, which you have, has the cross, the bullseye and the wreath. The loops on the bottom of the pin were for an attachment to hang on it which had the name of the weapon you won the pin with.
On the range you were given 90 shots at targets ranging from 25 yards up to 100 yards. You needed a minimum of 30 to be a Marksman, 45 to be a Sharpshooter, and 60 to be an expert.
I remember this because when I was taking basic training in the army at Fort Dix, New Jersey in 1965 I was a "Sharpshooter" and the hanger on my pin said "M-14"
A few years ago I dug a "Marksman" pin.
