As you progress in pet battles, you earn more and more stones, and pet charms to buy stones with. I remember being starved for upgrade stones when new, but that phase will pass. I remember I actually paid 2500 gold for a blue stone for my first Valk - I was so happy I caught one, I was delighted to be able to upgrade it at all.
If you are doing World Quests in Broken Isles, you will get enough charms to buy a stone every couple of days, I think.
As pets go, you will find it easier to capture a Blue Fel Flame of the breed you want than most pets. There are a lot of Fel Flames around, and they only come in 3 breeds. Compared to some pets, finding a Blue H/H would not be much of a grind.