Amato’s guide to relatively painless pets:

There are 3 abilities dedicated to Adventure/Hunt/Altar respectively. There are 6 lobby abilities, of which there are 3 clear winners.

Affinity raises the ability’s percentage value, not the grade. Never build a pet with A-rank abilities. Keep them around and separate, using them as-needed, or feed duplicate, content-relevant S-rank abilities into them to give them more value while you continue to look for the S-rank that you want. Building is easy, maximizing value is gated. If you have multiple different S-ranks and aren’t sure which to synthesize first, this is my priority list.

Hunt – Extra equipment > Double mats > Extra charm
Altar – Extra common > Extra greater > Extra epic
Adventure – Rare catalyst > Double AP > Extra side story currency
Lobby – Extra gold > Reduced equipment enhance cost > Increased equipment enhance XP

If you were to build a 3rd gen hunt pet with extra charm and double mats and then roll an S-rank extra equipment, you would have to either raise that fodder to 4th gen along with bringing the main pet to 40 to be able to make use of it, or hope for a one-in-a-million shot at rolling the 3rd ability you need when you first promote the main pet to 4th gen (like me!). Promoting a lv1 to 4th gen could take several weeks depending on what your fodder situation is, and you don't want to wait several weeks to use the best hunt ability by a mile.

To minimize this, you want to prioritize the first two abilities in each list, getting them both onto a 3rd gen synthesize, and consider the 3rd that’s listed as your luxury 4star ability.

Rationale:

Hunt – An extra piece of 85 gear or 20-40 mats in one run is not worse than a common charm. Easy.

Altar – The runes can drop on or above any level that's stated in their tooltips. Lv1 for common, lv4 for greater, and lv7 for epic. This means you can farm altar 10 with the common and greater abilities and have a chance to have all three drop.

Adventure – When it comes to side event currency, the extra yield is only useful when dealing with multi-week events that have large exchange lists and multiple currencies. Normal side stories are built so that if a player goes straight through it and then just runs hell 5 times a day for the daily quest, it’s enough to complete all the rep achievements, and buy all exchange items minus runes, which are worthless. Keep your A to S-rank side story ability on another pet and either feed it a duplicate S-rank catalyst ability to get more value when you are running side story, or just use it on its own when you actually need it the few times of the year that it will pay dividends. You will eventually bring your event pet to 4th gen, at which point you can fuse it with your adventure pet.

Lobby – This is the most important pet by far. You want your highest gold bonus active ASAP. Additional cost reduction is more value than increased XP but in this case you can affix either to a 3rd gen synthesize if you happen to have one or the other. Good and great chances are potent xp procs that also save gold but are wildly inconsistent. Take the permanent, consistent reduction every time.

To squeeze an extra 20 affinity out of a day that you synthesize one of your main pets, make sure you play with it first. Synthesizing creates a new pet, and allows you to play with it again for 300 stigma even though the higher affinity between the two carries over.