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since the men at arms equipment consists of hand weapon, shield, and polearm, are they allowed to use either a hand weapon and shield, or polearm without shield
Polearm is a halberd, yes? They are two handed. So yes, when you first begin any combat you can choose to either use hand weapon and shield or halberd with no shield. You can't switch during the combat.
Remember, that you can always use the shield for long range.
Any unit can choose what equipment it uses at any one time, so a unit equipped with shields will use them when not in combat to protect from ranged attack, then when they get into combat you have to decide which equipment to use. You have to stick to the same equipment until that combat is over, but are free to choose again at the start of the next combat.
Basically you can use two hands' worth of items. So, as strewart said, you can use the hand weapon and the shield because they only use one hand each, or the halberd on its own, since it requires two hands.
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so taking this into account. Its probably best to use the polearm against units that would ignore your 4+ save anyway (shield, light armour and combat weapon). Other than that I prefer the combat weapons... as it ads survivability to the unit.