EDIT 8/24: I've updated the build and touched up the description to match! I've been running this in Steel Path solo mission no problem, except for Excavation, I just can't seem to play that game mode solo =/
The ONLY game mode I don't recommend using Gloom is Defence with a group. You'll simply slow down and piss off your teammates!
Quick and Dirty DPS Build
One thing to note: This build is EXPENSIVE. 197,780 Endo is nothing to sneeze at.
You can find my Beginners Saryn Build here
And my Intermediate Saryn Build here
Growing Power, Blind Rage,Augur Secrets and Umbral Intensify for Good base damage, faster damage scaling and a high slow percentage on Gloom.
Stretch and Overextended for high range, making spores spread all over the place and giving Gloom a sizable AoE(37.6m)
Arcane Energize and Primed Flow for a bit of energy economy. You can run Energizing Dash as well (I do) for energy on demand.
Umbral Vitality for a big 'ol health pool.
Primed Continuity gives us more uptime on Toxic Lash and better drain economy on Gloom.
Exilus: There are many compelling options here IMO. For just starting I recommend Handspring, as nothing will kill you faster than being flat on your back while the enemies are shooting you. Cunning Drift if you want +15% Range(I don't think many of the "Drift" mods are worth slotting as they give you a marginal increase to the stat but you lose out on the utility of other choices). Mobilize is a great option for 5 points, giving you 20% increased Bullet Jump power and Aim Glide duration.
Giving Saryn Breach Surge from Wisp is something I've had good results with. The blind will buff your damage even more, give you double procs on the spore damage and help cc the enemies. The radiation procs from Breach Surge will also add another layer of cc, although really not all that important.
Giving her Roar is absolutely an option, you will slaughter crowds faster, but I prefer Breach Surge as it adds some CC to her kit.
Pillage is a compelling option for quick shield gate resets.
Primary; I use either the Kuva Bramma or Zarr, both of which are great AoE weapons.
Secondary; Kuva Nukor or Gaze Kitgun using Haymaker and Splat parts
Melee; Damn near whatever, I run the Glaive Prime.
Once you're done maxing this build, check out my personal Build with Umbral and Aura forma included! I, personally, think it's Saryn's Final Form!