the Brain Bugbear i'm having is that plate armour is marquee AC, but the movement debuff will come to the fore against enemies like zombies, probably in the form of a death. i've never really experienced BX in the players' seat, but i have futzed with it in solitaire (which is doable but made me miserable after a bit). zombies consistently have torn shreds through characters. they don't check morale, there's no reaction roll, they just throw themselves at the party until they're all killed. they're a joke if kited around by a party with a move of 30', but if improperly kited at a move of 20', it often devolves into a standoff slinging missiles. They have a statistical edge through their hit dice of 2d8 and plus one to hit. Their d8 damage per hit is pernicious. Their AC is nominal but with their higher health pool it's often a matter of keeping up regular DPR.
They always fail initiative, so that means they also fail pursuit, even if your movement rate is identical. But in that really grim set of circumstances, I was figuring I'd take a polearm and exploit its Brace. This doesn't work. There's no procedure for holding actions in BX and the polearm's Slow means you go last. The wording has this effect take a higher priority than failing initiative, which the zombies do. I'd be letting them roll for a free hit, where they'd have a 30% chance to inflict damage that sets me up for death from the next hit. Zombies' no. appearing means that's a single casualty in a group averaging 4-6, with an approximately 50% chance to score a hit. This assumes a sensible chokepoint, which isn't hard to set up. This is still folly. You can't beat an enemy who can't fail morale tests in a game of attrition.
Tentatively, I traded the polearm in for a spear, a shield, and some javelins. The fact my fighter has a sword goes without saying. Javelins are damn good, actually. It's the one handed action of throwing knives but the ranges are better and that can make up for my reduced movement. Shortbows are too expensive and take up both hands. I am anticipating a megadungeon where we're going to find a stable base camp after the fact, hence why our PCs are rolled up like it's AD&D (which honestly if the gm wanted a better shot at us surviving, they could bump our sorry butts to level 3 - BX combat just doesn't function until PCs have an actual health pool and the cleric can use cure light wounds). I will worry about needing to deal with outdoor ranges when we survive long enough to be outdoors. Now the action economy of drawing weapons varies, but it's still flexible to throw something downrange if the sword isn't quite handy.
The spear? Good in the instance where i might need the polearm