What to prioritize when powering up?

I would say that 15a is important for calculating breakpoints and would probably be priority if the IV's are close. Personally, I have a maxed Dragonite with attack 14 because it was my best IV one and then later maxed a couple more with 15. I don't use scanners to get best IV's and my best Kyogre was 14 14 14 so that is the one that I am working on powering up. I play the game to the best of what RNG gives me and don't worry too hard that my Mon's are not 100 IV's. I am trying to max one of each type and it will take me a while because I can't raid hardcore and therefore rare candy is truly scarce. I have decent mons to enjoy though.

I prefer higher overall IV as long as atk is at least 13, but nowadays I also pretty much always power to the max if I power up at all. If you want to save dust and only power up to breakpoints, 15 attack becomes much more valuable.

And as for your example of Kyogres, the answer is to power up both, but start with the one with 15 attack. Kyogre is so good you should probably power up 6 if you can.

I have been focusing on powering up a balanced team of 6 just like you do in the main games. I want to power up this team above level 20 first before I focus on anything else. My team so far is: Venusaur, Arcanine, Vaporeon, and Machamp. I'm thinking about adding Gardevoir to the team, so I just need to decide on one final Pokemon.

Basically I would recommend powering up Pokemon that you think you will have the most fun with instead just powering up 6 of the same legendary or whatever.

Interesting question!

I live in a terrible area for playing pokemon GO myself, where a pokemon like magikarp can easily hold a gym for 5 days... and I rely on solo raids for TM's, which means I don't get many at all.

So because of that, I'm not very demanding of the RNG and consider everything with a "your mon is a wonder" rating and egg like IV's worth evolving. If I then get a moveset I like, i power it up.

TM's... I do save those for the very rare and high IV mons only

I powered an 11/15/11 kyogre with thunder to 30 when kyogre was the boss because it was weather boosted and cheap to do so. I will eventually power my best 15/13/14 much higher and I will eventually use some TM...but I never use kyogre.

Attack IV is in general all that matters because defense and HP often don't sigficantly differ throughout power up levels.

If you want to be efficient in star dust, you value attack IV the most. (Gengar could be an exclusion)

It's a personal choice, IMO.

Attack stat is the most important to deal damage, so most people would power up not so good IV pokemon with 15 ATK rather than a really good IV with 13-14 ATK. But then, there are bulk points that allow you to use an extra charged move, therefore dealing more damage. You can only reach those bulk points if DEF and HP are high, and it turns out that a pokemon with lower attack deals in fact more damage overall, thanks to being able to release that extra charge move. This may only happen in specific cases. So, still the most efficient option to save stardust would be prioritise ATK stat.

On the other hand, if you are willing to over spend stardust in a viable and powerful attacker, in most cases, you reach the highest damage breakpoint several levels lower than 40. So you could perfectly get away by powering up a good IV mon with ATK <15 and that way still get the max base damage, better survability and use a few extra charge moves.

Personally, I prioritise IVs. Within the same IV range, I go for the highest ATK. I'm usually happy with 13 ATK and over 90% IV.
I wouldn't feel happy powering up a 15 ATK 84% mon (as in your Kyogre example).

Above 80%, preferably 13+ attack.

I prioritize having a broad bench first. For example, there are a bunch of raid bosses where machamp is the answer. It is better to have three level 30 machamp, rather than 1 level 40, because there is only about a 10% change in CP multiplier between level 30 and 40. 3 * 90% = 270% > 1 * 100% = 100%.

Once I have a squad of level 30 answers to every question I care about, I've started maxing out a select few mon. Here species matters more than stats. TMs aren't an issue for me, now, but before TMs, the rule was, "species > move set > IV". If TMs are tight, that rule still applies.

Maxing out candidates are the usual suspects: Mewtwo, ttar, kyogre, groudon, rayquaza, dragonite, machamp, ...

I prefer the ones with 15 attack, but only max out meta relevant and favourites with 93%+ IV. Below that threshold I would power up till level 30 or necessary breakpoint below level 35.

from lvl 20 to 40 it takes about 230 candies, from 20 to 30 thats only 66 candies.
So i prioritize having a full team before having 1 legendary powered to 40 as for the same candy cost, I can have 3 powered to lvl 31.