Armor will spawn randomly on synths depending on the difficulty level. There is only one way: run, search.
IGORss
Very simple. Taking off the killed synths, or when you get to the institute there will be a store of material support. In it you can buy heavy stock armor, in a few days you will return to the institute again and there will again be other elements of heavy synth armor. They randomly change by 1-2 elements. At the moment, this is, in my opinion, the most effective armor in terms of performance, it surpasses heavy combat armor in terms of characteristics. Sometimes it drops out on legendary super mutants, mutant hounds, scorpions, but this is very rare (I have a maximum difficulty level).
If you want to protect yourself specifically from ballistic damage (and there are already 4 types of damage in the game: energy ballistic, poisonous, radiation) - then you need leather armor. There is a choice here, and each armor is for its specific task, but I made a choice.
Of course, you need to pump it to the top on the armor workbench, and you can do without power armor. I attach a photo, pay attention to the characteristics. I don’t use any mods in principle.
photo of heavy armor synths