You don't necessarily have to throw all magic out, just read things like Cado's Magical Journey, which has some good stuff, and then maybe borrow some rules from the World of Darkness line of games for things like "Willpower" as magic fuel if need be.
If you want really precise distances, Toady has used 2.5 meters or 3 meters as a per-map-tile distance. Local tiles are 48x48 map tiles, and there are 16x16 local tiles in a regional tile. (One regional tile is basically 2 km across.) You can generally assume a steady, standard march can accomplish 30km/20mi a day, which is 15 regional tiles, or nearly all of a pocket-sized map. (Presuming you actually generated a map and are using that.) If you export a map of the world from Legends Mode in the ASCII character format, each tile is a regional tile, and in the detailed view, each pixel is a local tile.
As for weapons, if you're doing D&D-style combat, you could do something 2nd Edition-ish, and have to-hit bonuses for each type of armor.
For example, a spear might have 1d8 damage with a crit range of 18-20 (and make up an organ damage crit chart, not just double damage) and largely ignore leather or cloth armor, but take -4, -8, or -12 to attack rolls (or just adjust enemy AC by that much if we're really talking 2nd Ed) depending upon enemy armor quality compared to attacker spear quality. (Steel spear versus copper armor might be just -4, while steel spear versus steel armor would be -12, and copper spear versus steel armor = just give up. Consider it an "armor piercing" quality of 1 per metal quality tier, that cancels out a point of armor quality each. Armor of equal material quality to a weapon should have three more tiers of armor protection.)
An axe might be similar, but with less severe armor penalties, (-3, -6, -9, -12,) an extra "point" of armor piercing, crits only on natural 20s, and a bonus to rolls on the crit chart so they get more severe crits, including "severs".
Hammers would do something more like 1d6 subdual damage to non-skeletals, but have only -1, -2, -3, -4, etc. for weapon/armor discrepency, and two more points of armor piercing. When an enemy is down, head shots are coup de graces for lethal damage.
Fine, masterwork, artifact weapons are like +1/+2/+... weapons in D&D, bonus attack/THAC0, and armor works the same for bonus defense/AC. Masterworks are +5, and artifacts are +10, although they still abide by quality rules, so an artifact wood spear is still crap against armor.
Most other weapons are basically variations on that theme. A crossbow takes those extra turns to work, but is like a ranged spear with extra armor piercing power. Straight swords can either be used in spear or axe-style attacks (in terms of how potent armor is against it, and the types of crits you can roll) but with less damage and either a 19-20 crit or a half as good bonus to crits as an axe. Pikes are spears with a d10 damage die, but a -2 initiative roll, and a -1 attack roll for weight. Etc.