I'll try to answer this to the best of my ability, keep in mind that I have yet to play ultimate so some of this will be theory craft based on my experiences with PT in brawl, charizard in smash 4 and what we know of ultimate PT thus far.
First off, you should aim to be good with each pokemon. Being good with only one pokemon limits your potential and forces you to sacrifice the return stock invincibility advantage when you return to the stage after a stock loss. Ideally with PT you want be good in every MU with each pokemon and have one ideal MU with one of the three pokemon vs each opponent. So for instance you should be able to take on each opponent with just squirtle or ivysaur, or charizard. The reason for this is so that you aren't limiting yourself to a predictable metagame.
With that being said, pick your favorite pokemon of the three and focus heavily on understanding that character's strengths and MUs. You need an anchor fighter that you feel extremely comfortable with. You can still play the other two, but practice matches where you predominately use that pokemon alone to better understand the MU for that pokemon. Once you start feeling comfortable with that pokemon, you can then move on to the second, then the third, and then finally learn to use the character fluidly as one cohesive unit. The idea here is to ensure that you use pokemon switch as a powerful tool and not rely on it as a crutch. The only way this can be done, is if your opponent isn't able to read when you make your switches.
As for the pokemon themselves:
: a rushdown character with a powerful air game. He lacks range so you may struggle getting in on opponents that have good range or disjointed hitboxes. Squirtle doesn't have power, but his aerials should allow him to wall out recovering fighters. Fair and nair will be your best friends in this sense. He also has a decent grab game, though running grab in ultimate looks to be bad for squirtle if he whiffs. In brawl down throw killed at higher percents. From what I understand this has been nerfed, but either way when you grab you'll want to launch the opponent in the air at low percents or off the edge at high percents and use squirtle aerial game to keep the opponent from returning to the ground.
Watergun is an underrated powerful move. Besides being able to gimp hard in a game where recovering is harder, it can also be used as a spacing tool to put an opponent at a disadvantageous position. Withdraw is a an okay move that can be punished hard, use it sparingly. As for Waterfall, it has a decent sized hitbox and is a good enough recovery tool. You may be able to hit a opponent on edge with it by falling and UpBing past the platform. However if your opponent reads this attack you can be punished. Squirtle is vulnerable from hi upper right part of his body during this recovery.
:Your spacing character. Ivysaur wants to wall out the opponents with razor leaf, back airs (and ocaasionally nairs and fairs) and then go in for a punish when the opponent makes a mistake. First thing to do when you start playing PT; go to training mode and learn Ivysaur's UP B recovery. If its anything like brawl's it can be deceptive. A lot of people will tell you to not use up B to recover with Ivy because it is weak (instead making a switch to charizard and using his recovery). I would suggest instead to rely on Ivy's recovery alone at first until you have mastered it and then start mixing it up with charizard switch to Up B. Again its better to have a full grasp of each character.
Ivy's up air is a great powerful sharking tool. Up smash may be too, but it has a substantial delay. It is more powerful so save it for hard reads instead. Down air is also a decent tool and can spike (at least in brawl) if positioned perfectly. Personally I don't think Ivysaur should be ever be in a position where Dair is a good option as Ivy wants to stay on the stage for the most part.
Finally Ivysaur has a tether grab. It's not too bad, but its still a tether. Save it only for when the opponent is excessively shielding
:Your heavyweight. Charizard oddly enough, hates the air. You never want to chase the character too far off the stage. Instead focus on just not allowing the opponent to land. He also sucks at recovering without taking colossal damage. He however has a great grab and a kill grab at that (upthrow). he also has a decent combo in smash 4 at low percentages in downthrow to fair. Down tilt and forward tilt are also good tools and have decent spacing. Unfortunately down tilt was nerfed from brawl to smash wii u and looks to be about the same in ultimate. Still not a bad move. Try not to rely to heavily on side B, instead use it to change up your recovery or for hard reads (particularly against rolls).
Honestly I believe Charizard gains the most from working as a unit with PT as he has good survivability and has those powerful moves to finish off stocks, but isn't the best at racking up damage without taking a bunch himself.
