I'd like to preface this by saying that I'm not actually very good at the game, so most of my input is based on what I've seen from various sources.
Mewtwo's main problems are against floaty characters, Mario, and people with swords. Some people say Ganondorf is a bad matchup, but I think it is totally managable/we have an advantage if you can camp hard enough and not get caught.
Shiek is said to have decent matchups against floaty characters (bar Jigglypuff?). In Melee she was one of the easier characters to learn, so that might have translated to P:M. The dthrow isn't as good as in Melee, but it is still great for setting up tilts and works with (b?)throw as a DI trap.
Zero Suit Samus might be good for similar reasons of being able to deal with floaty characters.
Against sword characters, I like to use Link and zone them out. He also has the added benefit of having a sword himself.
Mario, Fox, and Lucas are decent all-around characters in their matchup spreads, but the latter two are tech-heavy characters and would probably work better as a main rather than a secondary.
I think Ivysaur is a pretty good choice as well and is my personal secondary, but I'm heavily biased on this point so I can't actually vouch for it.
From the characters you listed, I think Charizard would be the best choice, but I'm not really sure.