Many, many Mexican youth easily avoid service by simply "buying" the proof of military service.
One cannot move on to university or civil service jobs without it.
No surprise there.
In my experience the M16 is the most numerous (and desirable) military arm.
They are known as "R-15s" and there's even a popular music band named after the weapon. By far the most beloved rifle in Mexico--mil. and civilian.
Mostly army and federal police.
FN-FALs are to be seen frequently also, though not as many as M16s. Army issue only, I believe.
AK-47s, AKMs, etc. are very popular with state and local police. The "Cuerno de Chivo" (Goat's Horn, for the shape of the mag) unfortunately for them, is also popular with the local weed growers and trafickers.
Of course with these armed groups, expect to see almost anything with a barrel!
Never seen any type of H&K weapon in Mexico. It's beemn a few years. Must be fairly recent issue to military/paramilitaries.