Good video for beginners.
One of my sayings among friends is "Life is too short to put up with bad triggers".
Biggest mistake is cutting springs. Buy after market kits, they are cheap!
I'm a little concern when you say you are planning on shimming the hammer and trigger. Shimming should not be needed on a J frame meant to be carried for self defense and IF it was you have bigger problems than a DIY trigger job.
Since you asked, my advice is:
Polish (do not remove metal!) all metal to metal contact surfaces.
Clean and lubrucate parts.
Replace factory springs with after market kits (Wolfe's or Willson from Brownell or Midway)