The controls portion is only a small piece of "safety", but as an FYI, most safety vendors have canned application notes that describe how to utilize X product in Y situation according to Z safety rating: Estop with safety relay to cat4/PLe/SIL3, etc. It'll include wiring options, any DIP switch/software settings that are relevant, etc.
Personally, I'm a fan of safety PLCs, because it makes it easy to manage multiple safety functions, but there are absolutely systems where it's overkill. Just an estop and a light curtain? Safety relays could totally make sense.
Most of the standards that I've read encourage you to design out hazards first, control hazards you can't, and then put on the finishing touches with administrative controls (PPE, etc). Every standard involves a Risk Assessment to figure out what all the potential hazards are, during all phases of the machine (operation, maintenance, etc). If you aren't comfortable doing taking responsibility for this, don't. There absolutely are firms that will assist or do it for/with you. It is a great and admirable goal to go out and get all the applicable standards and figure it out yourself, just remember that you're allowed to admit you're a human being with limitations, and you only know what you know.
The safe thing isn't ALWAYS to just cut power; sometimes you need to use a very low speed, or maintain a holding current to prevent motion. This is something that has evolved over time in the standards.