I typically will install the cpu, RAM, and possibly cooler depending on size and space outside of the case then install as one unit just because it's easier. I don't bother with a grounding strap and build on a wooden desk or table on carpet and haven't ever had an issue, but ymmv.
I think the biggest thing is thinking through your cable management and routing to avoid redoing work and getting a clean build.
As for screws, it depends but I go for good and snug with a driver for everything that isn't knurled. I don't wrench down on them, but in a few areas finger tight may not be enough (or will lead to vibrations and rattling). Fans, radiators, PSU, and cooler screws all get snugged. Fans especially I've found can be tough to drive if they aren't pre-threaded (and most don't seem to be), the screw cutting threads in the plastic as you drive it means you can't go "finger tight".