Any character can use any weapon on the list below and be relatively proficient with it. Weapons are grouped by the die type they use for damage, and all weapons with a given damage type cost roughly the same amount of money.
dagger, sling, club, wooden practice sword
Damage: d4
Cost: 4 coppers
spear, staff, mace, bow, short sword, hand axe
Damage: d6
Cost: 8 silvers
longsword, battle axe, longbow
Damage: d8
Cost: 16 silvers
great sword, great axe, lance, halberd
Damage: d10
Cost: 32 silvers
Great swords, great axes, and halberds require both hands to use and so may not be used with a shield or, more importantly, a lantern. They can also be trouble- some in tight spaces.
Bows and longbows require arrows, which cost 1 silver for 20, which is also about how many can fit in a quiver. Bows have an effective firing range of about 50 yards, while longbows can shoot effectively up to 200 yards away. A bowman may fire up to twice as far, but with a -2 penalty to hit for the extreme range. A sling can fire as a bow, but the ammunition for it is free, provided the slinger has a chance to grab an appropriate rock.