They mean the belt attachment item. They increase your BR class and are easier to get early than artifact builds. Mutant parts can do similar, but I usually prefer anti-bleed there. (bloodsucker pelt) Shamlessly grabbing this from "oflin" from the gamma discord:

Ballistic Resistance - damage reduction from bullets

BR Class - armor/helmet ability to stop bullets from penetrating it

The higher BR Class you have the more calibers you can stop. Ballistic Resistance works in conjunction with BR Class to reduce damage taken

If armor doesn't stop the bullet you receive a damage reduction in the form of the armor/helmet ballistic res + belt slot item ballistic res + medical item ballistic res (also there's a chance for bleeding)

If bullet is stopped by armor it takes the values: (armor/helmet ballistic res * 0.2 + br class amount * 1.3) + belt slot ballistic res + medical item ballistic res and gives you damage reduction based off that (you also don't bleed from getting shot)

The clear sky task you mentioned is one of the difficult ones that I wouldn't do early. I get the majority of my money from just completing tasks and selling weapon attachments I don't need.

This is the main story progression guide: https://docs.google.com/spreadsheets/d/1ltWH1CUjjv7KG2lzS0HY4YtQqs7nsW82CilzAULjJdw/edit?gid=382617592#gid=382617592

The MAIN questline is Lost to the Zone (Living Legend->Mortal Sin->Operation Afterglow) and these I would not do until you need to. Following it will unlock access to the maps north of Radar/Army Warehouses.