sambrookjm: 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).
