Do IV's make a big difference in PVP? Which ones?

Hello, I am starting to get into PVP, especially with the GO Battle Leagues coming soon and would like some help in deciding which of the Pokemon below to use for the Great League from those who play PVP a lot. Will eventually do more after. Do IV’s matter? Using Pokegenie I have all the stats below. IV’s, Level, candy and rank by hashtag. Would like to use shinies and Bastiodon for obvious reasons but have lower rank and stat product, is there a huge difference between them? I have plenty of stardust so that isnt a problem but great to save where necessary. Or should I wait for better ones?

Altaria/1,978 candy
Swablu-IV-15/15/12-Level 25 #3398
Swablu- IV-2/13/9-Level 14 #271
Shiny Swablu -IV-14/6/11-Level 14 #3167
Shiny Swablu -IV-7/6/5-level 14 #3155

Bastiodon/167 Candy
Shieldon -IV-15/15/14-Level 20 #137
Shieldon -IV-14/11/11-Level 20 #57
Bastiodon -IV-12/4/13-Level 35 #567

^^As I have lower candy, Bastiodon looks better but apparently the Shieldon’s are better but won’t have enough candy. Much of a difference?

Medicham/2,152 candy
Medicham -IV-14/14/14-Level 34 #15
Lucky Medicham -IV-13/13/15- Level 26 #25
Shiny Medicham -IV -6/14/11- Level 27 #701

Recently, you can feel better about higher attack IV, because the Pokémon with the higher Atk stat gets to use it’s charged move first in the instance that both players are ready to go at the same time. That can be the difference between a victory or a loss.

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I have a niche PvP question, I recently got a 15/15/14 lucky Registeel. It is at level 30 at the moment, it’ll max at about 2441. It will take me considerable time to get the rare candy to max it…is there some level where Registeel is still top 10 ultra league BUT really only if it has 2 charged moves?

Should I stop at level 35, get the 2nd charged move THEN max it over time

I’m not seeing any of the Regis being worth what their second move costs. They’re a fun, dumb, one trick group of mons that can wall certain opponents terribly. Dumb because they essentially have one move, since Lock-On’s only purpose is to charge that move. It’s goofy using them and you’ll get some wins. But I can’t stomach that candy and dust cost for one of them unless you’re just swimming in it.

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Thanks for the reply, I have 75% of the main masters maxed and double moved. I have maybe 70% of the main greats close to 1500 and double moved. However, Ultra is not close to those percentages…mainly bc the 2nd move investment in that middle league doesn’t lure me into spending. At the least I’ll max this lucky Registeel, just to make me feel like I’m preparing for Ultra…MAYBE later they find a way to give Regis a multi-bar move and/or they give us a cheaper way to double move