I've played 4th through 7th editions of CoC roleplaying game. While there are some valid criticisms regarding the chase mechanics and a few other subsystems, frankly, IMO, this is the best version of the game thanks to the addition of the push mechanics, which create another opportunity for tension and drama at the table. The percentile based dice mechanics of CoC are easy to understand, easy to teach to new players, and are fast in play. Combat takes minutes, not hours. I think CoC is in many ways, the precursor to the rules-light games so prevalent today.
Is the game deadly? Depends on how the players approach the problems. If they're running into combat like it's D&D, they are going to have a bad time. But it's not a game of combat, it's a game of investigative horror. To me the most exciting part of playing CoC is seeing how many secrets your character can uncover, how deep into the bowels of the arcane mysteries of the universe they can crawl, before they become so damaged and deranged due to health and sanity loss, that they become unplayable. The more your character grows, the more damaged they become. It's an inverse progression mechanic and I think it works great... as long as everyone at the table understands what they showed up for.
I have not played the Arhkam Horror TTRPG but reviews for it do not excite me. It seems very boardgame-y to me, which might be okay if everyone at the table are boardgame players and are just dipping your toes into TTRPGs. But it seems like there's just one published adventure, a fixed narrative, and fixed characters. CoC has hundreds if not thousands of published adventures, play options in different settings (gaslight, ancient rome, modern, etc) and affords you the freedom to play the game/character you want.
There may be other systems better suited to running Cthulhu-type adventures. I am currently running and loving Mothership, but that's sci-fi horror and would require a significant overhaul to run a 1920's setting. I don't know much about Candela Obscura though it looks neat!
Anyway, in answer to your original question - Core Book and Investigator's Guide plus an adventure are plenty unless you want to run a campaign in a different time period than the 1920s.
Pointers?
- Never lock an essential clue behind a skill check. Or if you do, make sure that you allow a failed dice roll to mean "success plus a complication"
- Read this excellent article on the Three Clue Rule from The Alexandrian: Three Clue Rule
- Set expectations with your players that combat is deadly and their characters may not survive
- Don't take it too seriously. Some of the funniest games I've had have been running or playing CoC. Nothing eases the tension like a belly laugh!
- Have fun!
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