Squirtle fares very well against Ness. It's really sad. Ness is too easily gimped by Squirtle. Like Steeler said, water gun can be used on his double jump to force PKT2 usage. You can also push Ness or just cancel out PK Thunder. Squirtle is faster than Ness on the ground and he has better aerial mobility. Ness's b-throw is stronger than Squirtle's d-throw, but it really doesn't matter too much, because it only takes about another 30% for Squirtle's d-throw to kill as it does for Ness's b-throw to kill Squirtle, no DI and at a sizable distance from the edge.
Ness's fair is good, but honestly, if you don't predict and time when Squirtle will be in your face, you're pretty much not going to get the hit. Squirtle's aerial attacks come out a bit too fast and has less cooldown than Ness's do. Ness's air game is probably better for raw damage, but Squirtle can easily use two aerials and get Ness off stage, where he sucks at vs. Squirtle. There isn't a place in this fight where Ness has any upper-hand on Squirtle. Squirtle's ground game is just too fast for Ness's, and he can easily compete in the air. Ness's best responses are PK attacks, but if he can't land those, then he doesn't have much else going for him.
Ivysaur. Oh my god. I knew it was going to be bad just by comparing their attacks. Anyone who thinks Ness has an advantage on Ivysaur has lost their mind (or they just think that Ness is great and Ivysaur is not). Ivysaur outranges Ness pretty badly, but of all of Ivy's ranged attacks, the real ***** is bair. It COMPLETELY halts Ness's approach. There is really nothing Ness can do it about a SH or FH bair. PK Fire probably won't hit very often, PK Thunder will get canceled out, PK Flash will not work, Ness's ground game will not reach Ivysaur, and Ness's fair gets outranged, so Ness gets trumped. The funny thing is that Ivysaur doesn't even have to use bair; he can also use any of his B moves to halt Ness. Vine Whip is basically a smash attack that reaches at 45 degrees, Bullet Seed hurts big time and stops Ness from approaching from above, and Razor Leaf is a pain, because it can be used when Ivy is closer to Ness, since it's faster (and Ivy can retreat with it). Jab is better than Ness's ground attacks well; the only things that can reach are PK Fire, PK Thunder, and maybe a properly spaced dash attack... maybe. Ivy can grab-release -> jab, too.
Off stage, yes, Ivy can be gimped. PKT2 can cut through Ivy's aerials to hit Ivy. In response, Ivy can just Razor Leaf Ness for more damage or he can Razor Leaf PKT2 and safely cut the distance. Bair -> tether is a good edgeguard, too. If Ness comes from high up, he needs to watch out for Vine Whip. Ness can fight off Ivy effectively... if he ever gets past Ivy's attacks. However, Ivy's moves that are on top of him (nair, Bullet Seed) and those that provide disjointed hitboxes (every other of Ivy's aerials) can also stop Ness. Add in a good grab range, good throws, effective nullification of the PK Fire pillar since Ivy's weak to fire, and having equal or better killing power than Ness, and you have what I'm going to call a counter.
Charizard... hahaha, Charizard. If Charizard plays defensively, he's probably not going to lose. Flamethrower racks up damage fast, edgeguards the hell outta Ness, stops a lot of Ness's approaches, and clashes with PK Fire and then just overrides it. Rock Smash is incredible to use on Ness as well; it has strong knockback and it breaks into many highly damaging rocks. If Ness hits it, it'll break on Ness and hurt him anyway. Ness's Fsmash can reflect it for insane damage on Charizard, but it doesn't really matter because this move is excellent airborne. Charizard can shieldgrab ALL of Ness's attacks. I tried a dash attack, retreating fair, and Dsmash. Charizard can reliably shieldgrab all of that. Charizard's grab and throwing game, like the other two Pokemon, is incredible. He can force a ground break and then jab Ness right out of it. I don't know if WiFi interfered with grab-release -> dtilt, because I was able to shield it. I got hit by Dsmash a few times, but I don't know if that's a true follow-up as well because I shielded that eventually, too. There's nothing Ness can do about Jab, however. Charizard doesn't even need to use his smashes in this fight. They help, but they aren't even needed.
If Ness can get past Charizard's defenses, he can do well against Charizard in the air. However, he still gets outranged for the most part, and one aerial can stop Ness easily. Edgeguarding Charizard is difficult because Fly has super armor frames near the end (and it kills, so watch out Ness). Stick to PK Thunder because it works nicely on Charizard for the most part. Ness getting edgeguarded, as with the other two Pokemon, isn't too difficult. Flamethrower will slow down PKT2, cancel out PK Thunder, and stop a lot of Ness's aerials. Fair, when sweetspotted, is pretty much a horizontal meteor. Enjoy it. Rock Smash walls Ness as well. Bair kills very quickly if Charizard connects with the flame on his tail. It's a pain for Ness to get back. However, Ness does alright up close to Charizard.
Yeah, the Ness board probably isn't going to let me come back after this, but seriously, it's not a good fight for Ness at all. It's winnable, but it's really a pain. Be glad that (currently) nobody plays PT. As time passes on, we'll have more PT players, and things will be rough for Ness.
Final verdict:
60:40 Squirtle
70:30 Ivysaur
60:40 Charizard
65:35 Pokemon Trainer.