Do an image search for a pet battle cheat sheet that shows what types of pets are best to use in a particular battle. For example, critters generally have the strongest attacks against undead.
You can get tokens that level-up pets and ones that change greys, whites, and greens to blue quality by doing world quests.
Check out the warcraftpets site for lots of detailed info (This thing won’t let me post the link).
you can also use the trainees that are up during certain callings to farm pet stones
I have three of these at max level. They are extremely useful.
if you’re starting out, don’t buy your pets.
either catch them, or farm them
buying pets is for folks with gold to burn.
Have only 1700 pets have 200 in charters and guild bank lol
There is some good advise in this thread from others however I would like to add a few. The few pets mentioned here are good choices, you need Unborn Val’kyr, Read the comments, get cords and grab one, from WOLK. Any other pet that has black claw and hunting party or flock abilities. With these 2 pets with hunting party and or flock you can solo 90% of most pet masters.
A must have addon is rematch, it remember fights and can auto load teams when you click a pet master or a pet, you can also get rematch strings from comments in wowhead on each pet master or pet, there is few other sites that has like every pet master for past xpacs with all the stings to import. Rematch makes farming wq’s for polished pet charms very easy.
There is also guides on wowhead and another I use a lot is warcraftpets.com Hope this helps and good luck!
That’s good advise but some like Anubisath Idol and few other much needed pets are hard to get/farming dungeons and prices are not too bad.
Mission table gets tons of tokens you can use for the lvl 25 boosts
Which mission table? Also to get my “sea port” do I need to finish a particular questline for WOD? Can’t recall been a while.
Shadowlands
As for pet stones 
The addons you will (may) want are:
Rematch
tdBattlePetScript
tdBattlePetScript-Rematch
Get your pet strats from here
Also if you go to wowhead and lookup the battle you are doing, let’s use Cliffs of Bastion as an example
if you look at the comments you’ll find helpful tips 
A lot of us wait for what the community refers to as ‘Super Squirt Day’ (dates bolded)
https://www.warcraftpets.com/community/forum/viewtopic.php?t=16187
to level our pets. It’s when the WoD trainer Squirt shows up on a day during the pet battle bonus week.
I would suggest getting a pet with the weakening blow ability
to collect pets.
World quests in BFA and Shadowlands can give good tokens. Some tokens will level your pet others will change it to Rare quality. Mission tables in BFA and Shadowlands have quests that give tokens. Mission tables in WoD and Shadowlands have a few missions that give pets. There are many places where you can buy pets with tokens. Some nice ones are very easy to find in the wild. You want to have a pet catching set up so that you can capture wild pets easily.
I often will level pets in the Garrison in WoD. Especially during the extra pet exp weeks or Super Squirt days.
Already stated, but I want to emphasize: if you have any level 3 garrisons, there’s a quest to go get a special stone that awards an epic pet battle stone that automatically grants 25 levels to a battle pet.
I only did that on a couple of characters during WoD and then forgot all about it. Was SUPER excited to run back on my alts and pick up 6 of those bad boys in the space of 30 minutes just a couple months ago.
Open your map, click the magnifying glass next to the map pin. Make sure you have pet battles turned on, then you will see pet battle WQ’s.
I didn’t read the thread but i found the best way to get pet charms is with the mission table. BfA and SL mission tables both give like 16 pet charms per mission so the more characters you have that can do the missions the more you can get per day
Then if you have a pet menagerie in your WoD garrison you can trade the charms for instant level 25 stones
The pet menagerie once levelled also gives you a daily thats super worth doing for goodies
If it isn’t the lovely Chintzy! Where ya been my Goblin pal?
Is that a certain building? Haven’t seen that one before I don’t think.
Its trickier to unlock than the other buildings but big worth on at least one character
So more Ashran questing to get the BPs just like the inn and things? Just not sure how to “find / start” the quests though. x.x
If he wants to be the very best, then he has to do the tournaments. Level 1 pets will get slaughtered.
I didn’t see it but maybe it was said…when doing pet battle WQ’s, you actually do NOT want to use your biggest and best team because then the pets you fight also get to level up and gain their stronger abilities that also combo or otherwise are a much more significant challenge to deal with.
Use level 1 pets that have a basic attack that is strong to the enemy and, ideally, take less damage from their basic attack (or at least aren’t weak to it). By far the quickest and easiest way to deal with them
If you have other max level toons, you can do the WQ multiple times even. Just be smart enough to heal up before logging off otherwise you got a 2 minute wait before you can even use the NPC to heal.