In most situations resists are the most important thing. Each pet-type fills a specific role, though and understanding that role is essential to farming a top-notch version of that critter.
I would start with farming a mare... It's relatively easy to farm a good one because so little of their stats actually matter. Focus exclusively on resists when farming a mare. It's important to have physical, Fire and Energy as high as possible. Cold and poison aren't bad to have too, but they aren't as important (at least right now). STR makes next to no impact on the dmg output of a mare. HP helps a little bit, but not that much.
Since you want WW & dragons I would farm until you have one of each that's within 6 or 7 of max possible resistances. I would also make sure the WW is really high in physical, cold and energy. Make sure the dragon is high in physical, fire and energy. The reason I would look for these specific properties is that WW are the pet you will want to use when you're trying to be able to take cold and physical damage (and yes there are places where this comes into play and probably will be more in the future). Dragons on the other hand are pretty much a standard-use pet... It's not a bad idea to look for good HP on either of these pets as well, but resists are definitely the most important.
I think it's interesting you're not looking for a hiryu. Hiryu are excellent in some specific situations because of their monsterous hits along with the 108 wrestling and 70/90 phys/fire. Hiryu can be EXTREMELY powerful. Sure, they don't heal themselves and they won't ever do as much dmg as a 2 pet combo, but they certainly have their place.
For Cu, str is irrelevant. You only gain about 1 avg dmg per hit by getting a max str cu, which is pretty much irrelevant on a pet with a base dmg as high as a cu. Resists are the absolutely most important thing on a cu and HP are a close second (because there is a pretty high variance between min and max hp on cu). I focus on physical, fire, cold and energy resists on a cu. I don't have what I would consider a good cu because I haven't farmed them nearly as much as most other pets. Personally, I didn't worry about HP, but I recognize HP as being important on a cu. It is essential to have physical over 60 and cold/energy over 80 on a cu because those are 3 critical aspects that make the cu your best pet to choose in some key areas in the game. Fire resist is important because most damage spells are fire based, so having low fire resist on a cu will make casters tear it up a lot more. A good strategy for farming cu's would be to look first at the HP on it. If the HP are good (close to 1200) then look at the resists and see if they are good.
Good Rune beetles are exceptionally rare. The problem with rune beetles is that pretty much every stat on them is important for something. Resists are also extremely important and the variance between min and max on rune beetle resists are exceptionally high. If you just want a rune beetle that does pretty well, I would recommend focusing on physical, fire, poison and energy resists as your primary focus. HP and Int are the #2 priority followed by STR and then by skills. I haven't really seen much of a difference between a beetle that has low poisoning and a beetle that has high poisoning, but I think they are still important. I find that the best tactic for farming rune beetles is to first look at their barding difficulty. If bard difficulty is < 113, kill it and move on. If barding difficulty is 113 or higher, look at resists and see if they fall in your criteria range. The reason this is a good tactic is because bard difficulty is calculated based on the skills and stats a creature has. If the bard difficulty is 113+, the beetle will have high skills/stats. Resists don't come into play with bard difficulty, so you still have to look at them. My current rune beetle has the max str/dex and it destroys things noticeably faster than your avg rune beetle.
On to bakes... If you don't have bakes, you aren't playing your tamer to his/her fullest. They are a critical filler-pet because they can have up to 60/90/60/60/60 in resists (though I've never seen one quite that good). There is some debate on what is most important on a bake. IMO, resists are the absolutely most important thing followed by HP and then INT. I don't worry about STR because the difference in dmg per hit of a fully trained bake with min str vs a fully trained bake with max str is only 3 dmg. IMO, it's more important for the bake to be able to take a hit than it is for the bake to be able to do 3 more dmg. Int is pretty important too because that determines your mana pool and your spell damage. Even so, a max int bake only does 5% more damage with its spells than a min int bake.
So... Resists and HP are the most important because if you get a bake with high resists and HP, it will be able to survive almost any attack. My pvp and pvm bakes have high resists and HP. Neither one has ever died even when 4 or more mages were trying to kill them.
IMO, the most important resists are physical, fire and energy because those dmg types are the most common. I still think it's a good idea to have all resists as high as possible because you never know when the devs will introduce new critters that do new damage types. Also, having high TOTAL resists helps a LOT when you're fighting against things like shimmering effusion, which do 20% of their melee dmg to each dmg type. It's critical to have fire resist as close to 90 as possible, because that makes the bake pretty much shrug off all fire spells and damage.
I think it's safe to say that if I found a max HP bake with 60/90/60/60/60 resists I would be dancing in the street. Granted, a bake like that has < a 1 in 1 million chance of spawning.
