I understand the general idea about health, experience/proficiency points, and mana - but what I don't understand is everything else in the statistics.

For physical and magical damage, (i'm assuming you want the numbers low) so how do I do this?

For health, strength, intelligence, dexterity, and agility - (assuming you want high numbers), what stat do you increase the most first or does it even matter if you increase them in a certain order?

Sorry for all the questions. I'm just trying to learn and understand the game. Thanks!

We go over it in some detail here

For the Physical and Magical damage, these relate directly to how much damage your pet deals- the higher the number, the more damage your pet does per hit to the opponent. (read: the higher the better)
You want to align these with the proficiency tree you choose (Physical are Air, Earth and Water. Magical are Fire, Light and Shadow) and in turn, the equipment you give them (Strength for physical, Intelligence for magical. Relics are a bit tricky; they provide a large boost to either one or the other Damage type, or a much lower one to both. You should always aim to align the Damage type with the stats of the relic and the pet)

It should be noted that all pets have 'base stats' (the ones shown in the brackets)- these are the stats the pet has at its creation, and cannot be changed outside of philters used at hatching and nurturing as hatchlings. These vary depending on if a pet is Tamed, Fabled or not, the number of stars at capture if tamed (mana only- 1 star is 60 mana, increasing by 20 up to 4 stars having 120 mana. Fabled pets naturally have 20 higher, but all pets cap at 120 'base' mana), if the pet is Tamed/Exclusive/Generated with a given level of Essence.

What you put your stat points (level up points and proficiency points) into depends on what you want the pet to do in a battle.
A tank pet (generally the one in the middle of the screen during battle) usually has its points put into Agility, then HP
An attacking pet usually has its stats put into whichever type of damage it intended to do, with some also put into dex and/or HP.
How much is put into each stat, and exactly which, varies from user to user and pet to pet.

Once you get more gold you can easily reset and redistribute the stats- however, it should be noted that within the next week or two we are expecting the overhaul of the entire system that is intended to make it easier to use, and this stuff on level vs proficiency stat distribution will be probably irrelevant.