Engraving

Korean explanation of the engraving system’s hidden growth subsystem: https://soc.xd.com/kr/#/newsDetail?id=c1l22usbuaBN&lang=kr
Hawky made a spreadsheet of the info that is easier on the eyes: https://docs.google.com/spreadsheets/d/1ueuU4CLu5Uyscbn3M_DghQ3w0n7kjzLybiV0ud6gxlM/edit?gid=0#gid=0
Any individual engraving can roll 1-3 stat items. No two items can be the same (e.g. PATK% and PATK%), but can be similar (e.g. PATK% and PATK flat). You choose which to place on what according to engraving resonances and stat caps.
There's a big debate as to whether you should put swords on weapons or trinkets (wands on the other) for DPS units. Both sides have solid points. I went with sword on trinkets. The former statement presumes a paradigm of sword-wand being optimal. This is true for over 95% of all characters. Replace sword with cup as appropriate, and incorporate pentacles on tanks where recommended.
Pouring engravings into gear gives them experience in a hidden "growth" level.
These levels result in better engraving odds, both in chances of quantity of stats and in ranges of quality of stats.
You need 25, 100, 250, and 500 growth points for each threshold.
Common, rare, epic, and legendary engravings give 1, 2, 5, and 20 points per roll.
They cost 1, 3, 10, and 60 times the coins to engrave.
Higher engraving mats give better stuff, but it's not commensurate with the cost, and the odds are awful all around. You should be careful to maximize your gains.
Therefore, you should increase the hidden growth grade of your gear with lower engravings (up to 500 commons, but using some rares to save clicks) before spending the more expensive, more powerful engravings to roll for the good stuff.
Knowing which stats to chase varies according to which character you are equipping. You just have to read their kits and understand which stats they want. PATK-based DPS units want PATK above all else, MATK-based DPS units want MATK above all else, tanks generally want HP above all else, DEF stats are garbage on everyone that doesn’t get a conversion to a better stat from them (e.g. Ayishah or Yserinde), so on.