Dont bother with trying to loot set bonuses on random drops(plus most of the stuff on those two sets are garbage), that is just a milking from ssg to try and get you to spend money, plus they continually are lowering the drop rates. There are much more guaranteed ways to gear up.Not keeping up with gear is why you're falling behind as you level up. Here's the optimal gearset for level 16 as a brand new player:
Dread Isle's Curse gear (5pc):
Offhand: Power-Packed Barrel
Ring: Signet of the Earth
Back: Walking Ancestor's Shroud
Head: Walking Ancestor's Helmet
Trinket: Blue Raptor Feather
Feywild gear (6pc):
Wrist: Green Dragonscale Bracers
Belt: Belt of the Ram
Boots: Thorn Boots or Deepsnow Boots
Neck: Amber Pendant
Mainhand: Sceptre of Corrosion (I typically play a GOO/Acid warlock, but there's a similar scepter for each element).
I'm not including Sharn gear because you don't typically run it until level 17/18.
Feywild, Isle of Dread and Sharn expansions are worth the money. Typically Feywild and Sharn are available at a deep discount during Black Friday, so right on time for you.
The advice for the corrosion stick from planar eyes chain is good and something that would be worth trying to loot, but please dont be milked here either.
If you want to spend time doing time sink such as looting set bonuses there are better time sinks that give you guaranteed results now and for the future.
First, always decon and gather cannith essences and any collectibles along the way(dont be suckered into buying collectibles/essences from the astral shard auction house, its another game design to try and milk money). You can craft stuff that covers almost everything available on set bonus gear in cannith crafted gear.
Second the advice on the Spinneret is also good and should be something you spend time on (Slave lords chain) even now at your level go back and ransack it for ingredients. This gear in five slots will cover everything you can get in those two other sets and leave plenty of slots open for other gear that you can craft. Make yourself a slaver sorcery set. On the 3 fully crafted from scratch pieces you can put a feather fall, blindness immunity and fear immunity augment. This gear will be useful life after life.
After the two above you are likely to still have a goggles, gloves, belt, cloak, helm which you craft an assortment of things hopefully on blanks you have created that have augment slots on them.
Be careful on the forums, you will constantly find people trying to advise you to spend spend spend, this forumites can get away with saying anything in the forums because they have the support of the devs/SSG, your goal should be to enjoy the game and not have to empty your wallet. I think its great that you want to enjoy the game at your own pace with your own goals and running solo is perfectly fine, dont feel pressured or bullied by others to join groups.
If you want further info please feel free to pm me and we can meet up in game to chat, there are many things i dont chat about here where there are guidelines and censorship.
I do not think that new player will buy expansions until playing enough to be sure to stay longer in a new game (and he already paid for VIP).
Not to mention that all items must be farmed (repeating or astral shards "test your luck" payment, 10% drop rate per try on normal, 30% on elite - sounds like exciting experience for first timer to keep playing).
I brought here some non casual gamers and most of them left this game saying something like "if you must farm/pay like crazy for just passives instead of using your gaming skill to enjoy the game, then I am done here".
Still, this is good direction to start collecting gear if this idea of playing convinces you enough.
Onboard with this, you are bang on, loot areas sure but dont spend a dime on it and dont be reliant on gear. The whole reason the nukers have become prominent in the game is because it is an easier model for ssg to build gear that can be class dependent. The trick is that you are being convinced by other players that you need that extra 20 spell power to be viable, when really you dont.