Best party when you have all 8 you mean? My fav was Arthur, Doyle, Basso, and Lisa. They are the best attackers after all, no MP use needed. Especially if you get Doyle's Mithril Claw early, he's a beast. Of course if you manage to get Kusanagi's for Rodi and Akane then they would take up two of those slots, since they would quite often kill monsters instantly. And the most annoying monster is hard to pinpoint, the later dungeons have a fair share. I'd have to go with Hattari if only because of how hard they are to kill. But hardness wise most the Revisited Desire Mine monsters pretty much fit the bill. Still working on my FAQ btw if anyone is wondering. --- "What is a man? A miserable little pile of secrets."
for me my fav party will be arthur, lisa, doyle, and maybe rodi (for normal dungeons) or forte (for bosses).
annoying mobs got quite a few. One of those will be the creeping crab (/w 2 claws and main body) at enrich dungeon first encounter. That point of time still quite low-level and no great weapons. Later on there is a stronger version, which is as annoying as well.