You should upgrade the ability tree first as you stated, but afterwards you should, at minimum complete the basic tree (First four nodes) for attack, defense, and moves (Leave energy alone. There is no reason to touch it with so many characters to give points to). From there it's mostly up to you which tree you fill out first. Personally, I prefer to fill out attack, defense, move in that order since base stats are usually good enough to get you through most fights.
What I will mention is that for silver and bronze prize fights, a lot of the fights can be won with just the ability tree filled out, so once you figure out which characters you want to max out, it makes it easier to leave the rest with just the ability tree.
As for gold characters, think about which ones you want to focus on and save up points for them since filling out their trees can be annoyingly long due to their costs, but still follow the formula.
I can't think of a "good" character where you would do anything other than max out the talent tree first since the ability is a big reason why many of the top tier characters exist.
If you have any other questions or if I missed something, let me know.
i fill out the character ability nodes, then the move nodes, then attack, defense, then energy.
just my personal plan when I max out my characters - doing the attack nodes before the move nodes is perfectly fine as well, i just do the move nodes first so i can give more blockbusters and specials to a fighter. like @Gamma Ray said, ability nodes first, energy nodes last (even though the energy nodes are pretty helpful when you have them - its pretty noticeable when your special moves recharge in literally 15-20 seconds)
I don't think there's a rule for what to upgrade first. You should think carefully on a case-by-case basis. However, I can agree that more often than not you will want to go with the Signature Ability tree before extending any of the others. It is based on this SA that you will choose what to go for next, most of the time, because if the ability requires you to get hit to achieve the effect, then you know you need as much life as possible, but if it's centred around gear then you will need all the move slots and move points that you can get, and as mentioned above you would probably find the cooldown reductions found in the energy segment very useful too. Then if the SA is all about damage output or critical hits then you will go for the damage branch first.
Personally if I already have all the resources ready like points and gold, I do energy first since I'm not really using the character yet. I'm using one of my mains to carry the new character through prize fights and making their energy available ASAP to be used with my mains to max out their level.