I know this match-up pretty well from playing GenoSamus every week. So expect a lot of input.
I usually start with Ivysaur against a Samus.
Her B-Air breaks through all her Missiles, Uncharged Shot, and Half-charged Shot. So it's not hard to approach her at all.
Spacing Razor Leaf usually stops any Z-Air shenanigans.
Even though Samus can spike Ivysaur, keep in mind that Ivysaur's Up-B is a Meteor Cancel that Auto-grabs the ledge which nullifies that advantage and can put Samus in a bad position. (You should be able to grab the ledge even before her D-Air animation is over.)
The only things that you should have any trouble with is Samus' Charged Shot, Z-Air, & D-Tilt (The Fire Knockback gives Samus a viable kill move against Ivysaur past 110%).
Ivysaur out-ranges all of Samus' normal ground and aerial attacks so feel free to get physical with her if missiles are giving you any trouble.
You should switch to Charizard pass 100% or to get the kill since Samus has a very hard time killing him.
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Squirtle is my personal second choice against Samus.
He can easily weave in and out through Samus' projectiles. But Charged Shot is, once again, something to look out for due to it's speed & power.
Samus can keep Squirtle at bay for a time using Z-Air but other than that, her aerials are laughable compared to Squirtle's.
Her ground game is surprisingly solid when she's not out-ranged, and unfortunately she out-ranges Squirtle when she's grounded. Her attack speed on the ground is no joke either. You could easily be eating an F-Smash if you don't space yourself properly.
A little side note to remember is that Water Gun will gimp her pretty easily if she can't quite reach the ledge initially out of her Up-B.
When it comes to killing Samus your best bet would be either to gimp her (remember she can spike you easily offstage) or switch to Ivysaur or even Charizard. (D-Throw with Squirtle then an F-Air or B-Throw with Ivysaur will let you freely switch as long as she doesn't have a Charged Shot.)
Samus is heavier than she looks and won't be killed by a fatigued Squirtle too soon. It's possible to kill Samus with Ivysaur but not advised at high percentages. Samus' ground attacks are very quick and can easily punish Ivysaur's ending lag on her kill moves if dodged.
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Charizard is the worst starter in this match-up IMO. He's not bad, but the other 2 are going to have a much easier time than him.
Most of what has been said about Ivysaur applies to Charizard. His F-Air stops Missiles and whatnot. He out-ranges her normal attacks. Not to forget there's practically no comparison in terms of damage output between the two.
Z-Air is where the first problem lies. Charizard has no simple answer to Z-Air. Spot Dodging it and chasing Samus is usually his only option.
Charizard also shares Squirtle's weakness to Samus' D-Air spike but because Charizard doesn't have Squirtle's air speed to help him or Ivysaur's meteor cancel, he'll find himself at a huge disadvantage offstage.
But aside from that, Samus has a ridiculous time killing Charizard while Charizard can kill Samus fairly easily if he can get close. (Remember, she is a floaty character so Up-Smash and Rock Smash will be pretty reliable for kills)
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A quick summary since I don't expect everyone to read all that:
Ivysaur is the best starter IMO since has an answer to nearly everything Samus can do.
Squirtle would be the next best choice because he can slip through Samus' defensive game with ease, but can't reliably kill her.
Charizard get the short end of the stick in this match-up. He's not bad at all, but he doesn't have anything going for him against Samus besides his weight and power until she's within kill range.
