For me, it's currently a tie between weather vitals or weight. If it's a HW pup but not a hero, I kill it now. If it's a hero but not HW, I also kill it because I only value HW wolves. The only exceptions are when I need the bloodline, the wolf has a good defect/boost, or has the best talent/rarity count of the litter (with talents being the top priority between those two - only considered when I need the bloodline).

Edit: Don't mind me voting and posting before reading anything... oops-

My Top Threes

1. Heavyweight

- must be 130lbs+ because they'll be good for offense battling

2. Weather vitals

- must be a hero because they'll be good at catching the 5+ moves flavor texts in explore

3. Talents

- the more the better because it reduces the time it takes me to fully train, but I don't really care if it has 0 talents or 500. It's going to be trained for battle either way or killed soon if it won't be a battler.

So the only ones I really care about right now are weight and vitals. Everything else is just a bonus "oh hey!" unless it's a DH, HH, CS, boostXdefect or just a pelt defect. Those are of course valued for the same reasons that anyone would value them for.