Volunteer for extra training, shoot well, talk with armorer!
All these things will make you known as a shooter. Join the unit rifle team, volunteer for SDM training, and volunteer to conduct weapons training( CTT on rifle function and maintainance, PMI and such) If you stand out as a proficient and dedicated shooter, you MIGHT get a weapons upgrade.
That said, there is still the almighty MTO that states what weapon your position is slotted. With the extra training you MIGHT qualify for more. If you stick out as a competant shooter, they might TASK you as Squad Designated Marksman (SDM) There are some spots that are at commanders discretion, so having a reputation helps.
The armorer will tell you what you can and can't do with the weapons, but he can't work miracles. Keep your weapon clean(dirt and marks) and you will get his attention and earn respect.
A lot of new gear comes down the pipe when you move into theater. You will get most all you need. The armorer will get it out as fast as possible, but remember, he has all the weapons to do! on extra items, If the armorer can get it, and it makes sense, you will most likely get it. If you haven't earned his ear, push it up your chain!
P.S. - I am an SDM-qualified armorer.
That said, an M-4 can hit man-sized targets at 500m, so don't scoff at them too hard. If YOU bring it, the target will fall.