Hello, welcome to sin!
It's a good thing that you already know stuff like weaving, anyhow I'll answer your questions for you.
Stigmas for PvE: Dagger Oath, Lightning Slash, Apply Lethal Venom, Eye of Wrath, Deadly Abandon, Shadowfall. If you're up against bosses, you could swap Shadowfall for Sigil Strike. I don't know if you've already got your three additional stigma slots unlocked, but once you have them, you can get Dash and Slash, Venomous Strike and Shadowfall / Sigil Strike.
Stigmas for PvP: Dagger Oath, Lightning Slash, Fleeing Posture, Shadowfall, Ambush Raid, Shadow Walk OR Deadly Abandon, depends on if you like to be in hide a lot or not. Your three additional slots should be: Dash and Slash OR Apply Lethal Venom, your choice really as they're both good, take Dash and Slash if you're struggling to keep up with your opponents and Lethal Venom if you're confident you can stay near your opponents but just want that extra RNG DPS. Next up you can choose between Venomous Strike or Oath of Accuracy, you can use Venomous to help you cover silence or blind, or Oath of Accuracy if you're struggling vs Evasion set users, though I don't see that happening very often, and last of course, the stigma you didn't take yet because you chose one or the other earlier, Deadly Abandon or Shadow Walk.
As for PvE gear, I'd personally go for Dumaha Extends, since you'll be using them for PvP as well, and that's cost efficient! Doesn't matter in what hand you put them anymore I don't think, but for OCD's sake, put dagger in your left hand and sword in your right to make sure other sin's wont come cry at you for "PuTtiNg YoUr WEapoNs In thE WrOng haND". Also when it comes to actual armour and accessories, just go for either instance gear, or splen if you ask me. Not worth it to go for Pandora anymore in this patch.
For PvP Gear, like I said, you can always use your Extendable PvE ones, since you won't have a lot of reach if you don't have extendables. However, if you still want to swap to PvP weapons to when you're close for example, I'd just wait for 7.5 and get the new genesis weapons then, same for armour and accessories. In the meanwhile just farm Genesis Crystals and maybe Red Katalam if you're impatient 
Onto weaving, For PvE, I don't recommend you to weave after every skill, at least not until you get Kaisinel. Just most importantly, weave whenever you use Devotion (the blue buff) as this skill increases your auto attack damage by a bit. For PvP, I don't recommend you to weave at all really, nowadays, once you get gear and your daevanions, you mainly just want to focus on spamming your skills fast and in the right order. Try to take advantage of your Red Ambush Daevanion's 100% crit rate to use your Whirlwind Slash Daevanion, Surprise Attack, Dash and Slash (if you have it), etc. I could write you entire rotations but I'd be here all day, but hit me up if you really wanna know some rotations, though in pve I just kinda spam everything and make sure I spam that red ambush + burst skills after.
Regarding manastones, I'd honestly just go for full Physical Attack, since you already have a lot of time where you 100% crit with your Red Ambush. You CAN put some Crit Stones if you must, but honestly, 25% is more than enough if you ask me. Like said before, just use burst skills after Red Ambush.
70-120ms is not great for a sin, but it's not awful. You can pvp with it, but I recommend you try to get better ping by using a ping reducing program like ExitLag, Battleping, etc. You can use many of them for free by using new trial accounts every week or so.
Of course it's normal to be nervous! You're new to the class and you're not sure what to press next. It's completely normal and you shouldn't feel bad about it. This will get better over time, once you're more confident in your own abilities and once your muscle memory starts to grow for sin. Just playing is the answer to this if you wanna get rid of it fast, regardless whether it's PvE or PvP! Also make sure to use keybinds, if you're going to click, sin is just not for you!
Well there you go, I don't really have any more tips I can quickly write down and I gotta run now, but feel free to leave any other questions you have and I'll respond ASAP 
Good luck & Enjoy!
