For Alm and Celica specifically, the best weapons for them are actually the ones exclusive to their very own characters. For Alm, it's his Royal Sword, found deep within Desaix's Fortress. For Celica, it's her Beloved Zofia, which can actually be forged from the Golden Dagger.
When it comes to swords for Mercenaries, the best one found early in the game is the Lightning Sword. It can be found on Alm's Path in Act 1, and it's a very strong sword to begin with. Later in the game, the Silver Sword and the Brave Sword are the best among the bunch, as well as the Zweihander. As for swords for Priestesses, only the Ladyblade is worth using (and mentioning).
If you're looking for the best lances, the Silver Lance and Rhomphaia are the best options you have. The Rhomphaia is very rare and you'll only be able to obtain one within the game, so give it to your best lance user and give everyone else the Silver Lance. As for your best choice when it comes to bow, the best one, and perhaps the best weapon in the entire game, is the Killer Bow. If you can obtain four or five of these, though very hard to accomplish, you will have one piece of the strongest team known to man.