For this one, I'll limit the criteria down to characters whose best weapon is a heavy gun. This will eliminate the PSIII heroes for their use of Needlers, and the PSII men, Rolf and Hugh, since they can't go higher than lighter guns, a Sonic Gun, and Acid Shot respectively. That leaves us with Odin, Rudo, Kain(Laser Shot,) Wren PSIII, Wren PSIV, and Demi.
This one's a tough one for me, (avatar!) I'll eliminate Kain immediately because he lacks a brain capable of intelligible speech, and can't build; he can only destroy. So he's gone. And for Demi; she was imprisoned by Zio. That's weak! I love Wren PSIII's versatility to transform, but he's as interesting as a brick wall in the couple of lines we get out of him. He might mindlessly follow any male Orakian for all I know.
To have a party without Rudo in PSII is just nuts. He's so powerful that he can beat the game by himself, but I don't like his purpose. It took a tragedy to get him motivated. Odin is the opposite, he didn't need a personal tragedy to get him out fighting for what is right, but finishes with less HP than EVERY character in PSI. So...
Wren PSIV gets my vote. He joins the cause to fix what has gone wrong, never deviates, (ah, logic!) and he is the lynch-pin of the party. He's got it all!