So one of the easiest answers to the question of where your character picked up a lot of their combat, and a number of non-combat, skills is to have them come from a country that still has a mandatory military service. Numerous countries such as Israel, Singapore, Finland, Norway, Chile, South Korea etc. still have it today. So what sort of skills do people think a PC would learn in their year or two of service and to what level? Having had no real experience of the military myself figured I'd turn the question over to people that have, either regular or conscript.

Assault Rifles
Hand grenade throwing
Some athletics
A military specialisation - heavy weapon, tank driving, artillery, radio, maintenance, etc.
Some survival.

I suspect conscripts would leave with a skill of 1, 2 max in their military skills if they did not see any combat.

don't forget bureaucracy and if you go by older rules, ettiquette (military)? I can see them having to deal with the system.

avoiding duty assignment: 3
claiming you got a conscience as soon as you actually have to go to war: 3

Maybe this stealth group or at least infiltration - wilderness (or infiltration - urban if trained to city combat) and outdoor skillgroup

And if for some reason you became mp (military police) then maybe you have skills like these, at least basics of these among others:
Pistols
Close combat /Unarmed combat
Close combat/ Clubs

If you are specialist like sniper, then maybe there is thes among other skills
armorer - firearms
stealth group
longarms -sniper rifle

other skills you may have trained:
Parachute skill
Perception
first aid (and maybe specialisition combat wounds if medic)

Officers may have also basic skills of pistols, small unit tactics (?),

Im putting in my vote for 1-2 for non combat troops, 3-4 for those who see regular combat, and 5-6 for the elite of the elite.

As for skills, all should have (at least)

Automatics 2
Pistols 1
First Aid 1
Close Combat 1
Athletics Group 1

Add/Increase skills depeding on individual role. Some will have heavy weapons and gunnery, while others will be better at Pilot Groundcraft or Watercraft.

Gear maintenance (weapon and otherwise).

Engineering (latrines) 4

A friend of mine is currently in Hawaii acquiring what he has dubbed the "Piracy Skill" - a naval class on "Visit, Board, Search and Seizure." Apparently, he's been spending his time running around with SMGs and looking through crates and cabins for 'phat lewtz'. Or so he tells me.

Some days, I really wanna be in the navy.

Then I remember I don't wanna put up with it when I'm not playing pirate.

I'd say 2-3 on core skills, probably automatics 3 for infantry. We do train that stuff a lot, even though we don't see combat, and use laser simulator gear (used on actual weapons, so you can train 1:1 in the field) as well as live ammo/grenades in exercises.

(Fun fact: in Switzerland, conscripts keep their assault rifle and ammo at home. Shadowrunners, beware.)