Weapons with stats are much harder to teir up then clean weapons. Usually you start with NPC jewel to +1, use regualr jewels to +4, perfect one to +6, regular again to +10 and prefect one for last two, to +12.
So far I've seen only perfect +16 one, and use them. (never was found of gashas

)
As for pet & eggs, there is
very helpful tutorial on pets.
Basically, for production pet, any pet will work. Just get pet of any element, purchase tools from pet vendor and make it produce it.
For fighting pet and every day companion you like to get Holy pet with element that will complement your class choice.
Once you have Holy pet, first thing is to rise the Aptitude without severely rising it's level. Blue Rune Eggs (very expensive) are good start, to 90-something. After that you have to chain-merge pets of the same element and use training points you get to level aptitude. (1000 training points for 1 aptitude) But at this point you already know that rising good pet is very expensive and most required item is Golden Eggs. You can either farm them (hate that), get them from AH (again, back to expensive part) or hope that Mr. Owenstein (NPC that used to sell them) will be back in business.
Pet's do help a lot, for example my current playing pet is only level 17 and gives me over 1K HP, 350 inteligence (which translates into 700mAtk) and a bit less then 300 Wisdom. It's fire type (for mage) and transformed into Parrot (good buffs for Mage).
Very expensive, but as well, very rewarding.