I almost always have Rudo and Amy in the game. Um, other than that I switch through the other characters. If you have two Storm Gears (by the time you complete Menobe, that is), any of the weak characters will have fairly good weapon choices for the rest of the game and you can load them down with armor without equipping weapons.
Anna is really useful for walking around Skure, Crevice and the Dezo landscape. Her slashers have a definite advantage to the multiple enemies like the weirdo orangutans and gross rabbits. If you're not into level grinding, take Anna. She won't be as useful technique-wise, but she has better level-up gains and her weapons are probably the third most useful, behind Rolf's and Rudo's.
Kain becomes less useful after the dams, as there aren't as many mechas on Dezo. However, like Anna he's pretty strong. She's more agile, though, and has a weapons advantage. Recently I heard that Kain's mech techs work on the supernatural enemies, and I can honestly say I've never tried using them against fiends and what-not even though I've played the game about a billion times!
Shir... eh. Her biggest advantage is her agility. She's just as agile as Anna (maybe more), which makes her a great items user. The game royally screwed her out of decent endgame weapons because the Laconian Dagger's stats are bugged. She does learn useful techs, but takes forever to learn them.
Amy and Hugh are the tech gods of the party, and because she can equip the Nei Crown and the Nei Cape, you can keep Amy equipped with two fire staves and she'll still have fairly high defense stats. Her defense and healing techs are her biggest boost to the party. Hugh's vol and savol can be both frustrating and life savers. Amy and Hugh have pretty poor stat gains, and Hugh will die from a Shadow just looking at him wrong because for some reason he can equip almost none of the good armor. If he's low-level by the end of the game, the Nei Shield is a must for him.
Whew. So anyway, I use Rolf, Rudo, Amy and switch out the other characters. If I wanted to get through the game the quickest I'd probably take Anna.