Is there a difference between the various kinds of weapon beyond simple damage? For example, is a mace better at "smashing" Skeletons or Golems than a Short Sword would be?

In D&D, polearms like Spears and Halberds are longer than normal weapons, and thus can hit enemies further away. Is the same true in Bard's Tale, or are bows and spells the only attacks that can reach from the back row?

Bowsm thrown weapons (like spears, if they appear in this game) and spells are the only ways to hit from the back row, or to hit enemies more than 10 feet away. Well, aside from having a rogue hide and backstab an enemy (a strategy that works *really* well in Bard's tale 3).

Some items do have special properties; for example, some weapons cause status effects (although, unless the remaster changed this, the only status ailments that affect enemies are stoning and death). There's also a weapon that gives its wielder unlimited bard songs, one that regenerates spell points, and one that reduces spell point costs. There's also weapons that can be used as items to cast spells.

Also, don't forget that other items can be used and sometimes provide you with attacks; the Fire Horn, for example, allows its user to breath fire (the pre-made Bard starts with one). Just be aware that such items have limited uses; the Fire Horn, for example, will (in the remaster) break after 50 uses.

Note that Halberds are the most powerful non-magical weapon, and the most powerful weapon you can buy at the start of the game, so it would be a good idea to buy them for every front-line character who can equip them (though Monks will stop needing them around 6th level or so).

I could also mention the Shield Staff, which, while only slightly better than the Halberd (and not as good as some other weapons) has a property that will be immediately obvious when equipped (hint: the name should give you a clue); in classic versions I like to give it to my Hunter (if I have one), because damage isn't important here.

Unless it's been implemented in the remasters, weapon type does not matter.

In BT 2 and 3 weapons could have different range.
Halberds were 20', IIRC.
There were also returning weapons like Boomerangs, and various Horns used by Bards, all with different ranges.
So don't worry about not being able to hit distant enemies.

The remaster gives you the min damage, max damage, and the bonus to hit, so you should be able to tell which weapon will do the most base damage.

Weapons you will want at some point in the game:
Mages - Mage staff. Regenerates their Spell Points while wandering around, and also at 1 SP per round of combat. You can find these in Kylerean's Tower, and the first three floors of Mangar's Tower.

Bard - Bardsong. I believe this gives you unlimited Bard Songs? You can get this pretty early on. Kael's Axe is also nice, as it poisons the enemy you hit.

There is a Crystal Sword found in one of the dungeons that you will need later on the game to permanently kill a creature that's blocking your path. I gave it to my Paladin, as it's a pretty good weapon early on.

Monks - We don't need no stinking weapons! :)

Death Daggers do a critical hit, and Stoneblades stone the enemy, so damage is irrelevant here.

Rogue - Thief Dagger gives them a better chance to hide, while a Shield Staff will held their AC when they fail to hide. My rogue was almost always the one that needed to be healed/resurrected because he had the worst AC in my party.

For Mages, there's also the Conjurstaff, which cuts spell point costs in half; not that important in BT1, but in BT2 and BT3, spells can get quite expensive (one spel in BT3 costs 250 SP!). (With that said, if everyone but your wizard is dead, it might be worth equipping the Conjurstaff before you start casting Beyond Death on everyone else in the party.) In at least some classic versions of BT1 and BT2, the Conjurstaff need not be equipped to function; in BT1, Mage Staff + Conjurstaff gives you effectively unlimited SP (so no need to visit Roscoe's).

For Bards, the weapon you're thinking of is the Bardsword; in BT1, the Lak's Lyre also has this property (and in BT2, there's the Song Axe). In some classic versions, you don't even need to equip these to get the benefit. Does the Kael's Axe poison actually work on enemies in the remaster? (Status ailments other than stone and death don't affect enemies in classic versions of the trilogy.)

For Paladins, there's also Pureblades. The Pureblade is almost as strong as the Crystal Sword, and (in BT1 only) it can be used to cast Flesh Anew.

in BT2 and BT3, it's worth noting that Monks can use the Staff of Lor to cast Restoration. (In the remaster, you might need to enable the Legacy Mode option that unshares the party inventory for this to be worthwhile, assuming that option lets you use items that aren't equipped, as was possible in many classic versions.) In BT1, that staff is only usable by lesser spellcasters (not Wizards, for some reason).

For Hunters, if your critical rate is high enough, you don't need a weapon for damage, and can therefore put something like the Shield Staff in the weapon slot. (The Shield Staff is actually not that bad as a weapon; it's slightly stronger than the Halbard.)

Note that, at least in classic versions, if you somehow get a Death Dagger, it won't transfer to later games in the series. Stoneblades don't have this issue (though the easiest place to get one in the trilogy is in BT2's Grey Crypt; most of the enemies there can't hurt you if your AC is good enough, and the dungeon is easily reachable).

You're right - I meant Bardsword. "Bardsong" was a Freudian typo. After all, how many times do you actually talk about weaponry for bards, as opposed to their songs? :) Kael's Axe does poison your enemies in the remaster. You don't know how many points of damage it does a turn, but at the end of each round of combat you get a message saying "Monster *** takes some poison damage." if you hit something with it. The poison damage can kill them, as that happened to me a couple of times when I was doing mass party defense so my mages could regenerate their SP in combat. (They took out the Party Attack method of doing that, which was always a fun exploit.) I don't know if the poison damage stacks for each attack if you hit something multiple times.

Spell costs didn't really matter as much in BT3 because of Harmonic Gems and Flare Crystals, both of which automatically restored all of your SP. DIVA and NUKE were both super expensive, but a single Harmonic Gem took care of that no problem. I believe there was a staff (Yellow Staff?) that restored 2 SP/round in that game as well. BT2 was a bit trickier, although there you only really needed to worry about ZZGO for 100 SP as the most expensive spell. (I wonder if you'll need to hit the Destiny Stone in the remaster to "officially" find out what the Dreamspell code is?)

My party this time through didn't have a Hunter (it was Monk, Paladin, Bard, Rogue and 3 Mages), so I have no idea how they work in the remastered version. If weaponry is optional, then I'd definitely equip one that helped out their AC, since they can't hide like rogues, and (presumably) can't wear the heavy armor like the warrior types.

The DOS version of BT2 actually requires this. There is one byte in the DOS character file that acts as a bitfield with various flags. For example, one flag indicates that the character has passed the battle test; one is for the Destiny Knight; another is set if Lagoth Zanta has been defeated (he won't appear again); and there's one flag I call the Dreamspell flag. If the flag is not set, and that character tries to cast the Dreamspell, the spell will fizzle and 100 SP will be wasted. This flag is set (for everyone currently in the party) when you step on the square that tells you what the Dreamspell's code is.

Actually reaching that square isn't too hard if you have Speedboots (optionally a Nospin Ring), as you can enter the Destiny Stone early if you know the answer to the riddle. The Grey Crypt (where both items drop) can also be reached early, and the battles near the entrance aren't that bad; if your AC is good enough (in the 2GS version, Sanctuary Score gives your party -12 AC), the enemies can't hurt you, except the one that breathes fire, so it isn't that hard to farm top tier items this way. (In the 2GS version, Dragonwands and Flame Horns work well here; in the DOS version, those items aren't that strong, but Masterwands will work.) I believe that the Apple 2 version had a bug here; the staff would only restore 1 SP per round. The Commodore 64 version (my preferred classic version for BT3) has this bug fixed.