So, the vast majority of my playtime has been Saryn Prime. I love the frame, love the abilities. One thing I've learned is people all build her slightly differently in some places. I tried finding a be-all-end-all build, but ultimate I customized her to where I felt comfortable.
As of right now, this is the build I use for the vast majority of things: https://i.imgur.com/Lp8divR.jpg (I accidentally snipped it off, but rank 3 energy and arcane guardian)
If you want, these are the weapons I like to use with her the most:
Ignis Wraith - https://i.imgur.com/3%&^M75.jpg (If you don't have a good Ignis Riven, take Vigilante Armaments with this build)
Ignis Riven - https://i.imgur.com/G70DMOB.jpg (Not the greatest, but after changing all my mods around, I found this riven gave a massive DPS increase overall when I dropped Vigilante Armaments)
Synoid Gammacor - https://i.imgur.com/4dMBN0g.jpg
Nikana Prime - https://i.imgur.com/hHP4PwQ.jpg (I used to use Scoliac, and overall Scoliac is probably better. However, I had to fashion frame with the Nikana Prime since it's Saryn's signature melee weapon! I used to use Tranquil Cleave stance for the rapid quick melee, but with the melee changes I have found Blind Justice is just insanely better overall.)
Feel free to ask me any questions you may have. I absolutely love this frame, and play her a lot more than I probably should. Love my Saryn! https://i.imgur.com/79ybvrI.jpg