Never been a healer before in any game and I'm giving it a try for the first time. My initial, gut reaction is to prioritize critical rating since this would be more force cost efficient; however, I am not familiar with the subtleties of these stats or hootnannies.

In addition to that, are there any skill proficiencies that I should avoid or pursue?

Any critical rotations that I need to utilize?

Beyond that, any other general advice would be wildly helpful; thank you!

You might have a better chance to get an answer for this if you post in General Discussion.

(I can't help. I don't play healer any more.)

Actually, I think Dianiss' guide on the dulfy archive covering 5.3 changes is still a good guide for beginners:

https://web.archive.org/web/20200225223819/http://dulfy.net/2016/12/28/swtor-5-0-seer-sage-pve-guide-by-dianiss/

Also, while it goes over medicine operative, its a good guide for general healing principles and philosophies:

https://www.rambol.net/home/2017/12/18/medicine-operative-pvp-guide-by-hottie

And, because it is the most recent, here is the guide on Vulkk's site:

https://vulkk.com/2020/05/16/swtor-6-0-seer-sage-pve-guide-by-endonae/

I don't link these as evidence of their absolute truth, but rather as a starting place because you said you are new to Sorcerer healing and healing in SWTOR as a whole.