Is Engineering or JC the go-tos?
Jewelcrafting is mainly used to prospect adamantite ore and make steady talasites. Other than that, the usage will be defined by your build. There is quite the variety of gems you can obtain. Refer to this guide for additional information:
https://xpoff.com/threads/lvl-20-f2p-gems-and-jewelcrafting-guide.95274/#post-1256589
As for engineering, it is definitely one of the most important professions, if not the most. It allows you to tinker your cloak with a glider (the slow fall you mentioned), belt with grenades, heal, shield; you also need it for the ghost dragonling trinket and the socketed goggles if you go for those. Quite mandatory to have engineering really. Jewelcrafting can be dropped after you're done with the gems you want.
Generally, the "endgame" profession combo is engineering/alchemy for the majority of people. The reason for that is because the tinkers and things you make off of engineering require you to have it in order to operate them and alchemy has
https://www.wowhead.com/item=75525/alchemists-flask, which gives +9 main stat, scaling to +12 in BG's. Important to notice here, however, is the fact that the flask requires vanilla alchemy 300 to be made, but only a level of 1 to be used. That means you can safely drop alchemy after the flask is done and work on whatever profession you want to, then drop it and pick up alchemy again.
Is JC the only way to add some sockets to their rings?
No, socketed rings come from pure grinding. It's an upgrade proc, you can't control when it happens. All you can do is genocide legion hyperspawn spots in hope for a ring to drop and upgrade with a socket. That is usually done with a character that is either level 24 or 25. Make one and slaughter shit. Refer to this thread for some tips regarding ilvl 28 green boes farming:
https://xpoff.com/threads/best-places-to-farm-ilvl-28-in-nazmir-drustvar.94794/
I recommend the kobolds in Skyhorn at Highmountain, pretty solid spot because it is compact. There is a shit ton of mobs to kill, they hyperspawn like crazy and you can easily pull packs and packs. There is not much need to walk around like a madlad. I recommend Arcane Mage for the job, the spec decimates trash packs in no time. If you feel like the mana consumption is too high and you have to spend time eating food, then go Frost. Blizzard is excellent to control and AoE down big packs, as well as Ice Lance being a phenomenal tool to pull mobs fast as a motherfucker.