How would you judge the relative usefulness of animal companions?

[SangoProduction]

What are the most vital statistics to use, in order to sort the vast swathes of animal companions, and what priority should they have in ranking?
My first thoughts on vital statistics were, in no particular order:
1) Total physical stat bonuses + natural armor,
2) #of primary n.attacks + 1/2# of secondary n.attacks
3) Aquatic, land-bound or amphibious
4) Size
5) Level until advancement
6) Notable senses and special properties.

[liquidformat]

What are the most vital statistics to use, in order to sort the vast swathes of animal companions, and what priority should they have in ranking?
My first thoughts on vital statistics were, in no particular order:
1) Total physical stat bonuses + natural armor,
2) #of primary n.attacks + 1/2# of secondary n.attacks
3) Aquatic, land-bound or amphibious
4) Size
5) Level until advancement

So I created an excel sheet listing all (mostly all?) 3.5 animal companions (https://docs.google.com/spreadsheets/d/1VPLlQd6jAkI2rFnd2-NA-POzNUlM-Mg5gPSroZGJ05A/edit?usp=sharing), highlighting the ones I thought were good for their level adjustment. It also has familiars and mounts on their own tabs, though haven't finished those sections yet.
Anyways I think:

Total physical stat bonuses + natural armor, plus an adjustment for the few animal companions that are magical beasts
#of primary n.attacks + 1/2# of secondary
special abilities - things like pounce, blind sight, and so forth are major reasons to choose a specific companion
mobility - flight, climb speed, land speed, burrow, swim, water only, amphibious
size - sometimes bigger is better other times small is better this one is a sliding scale
Level until advancement - what do you mean here, are you talking about level adjustment or size increases? in 3.5 whether animal companions gain size increases is pretty debatable in pf it is a straightforward metric though.

[SangoProduction]

Sorry. I didn't tag it as pathfinder originally. Level of advancement is the level it requires before advancing to the next stage. Often either level 4 or level 7.