I would suggest starting with the 100m battle sight to see how well you group with that rifle. The peep sight is designed for sniping with a smaller peep aperture. The standard battle sight is what you should find on the M16 and you should familiarize yourself with that.
Long before I joined the Army in 68 I had qualified with open sights on old battle rifles for hunting in Colorado. I shot a fair number of game out to 250 yds with an older No1Mk3 303 (Mauser type 'V' sights) and then upgraded to a No4 Mk1 with the peep battle sight and did a whole lot better. By the time I hit Basic I had already familiarized myself with the use of the peep sight and both scored 'Expert' in marksmanship and do not believe I ever missed when I took an aimed shot.
Test yourself and be hard on yourself sniper, it will serve you well.
One more thing - see if you can get yourself into sniper training and keep that handle as a mark of qualification. Mikey.