Horror gaming in older systems such as Call of Cthulhu often does not work as intended because players don't follow the tenets of the genre. Whereas the first stop on many a PC's journey is the gun shop, arming up is usually a last resort for characters from cosmic horror, and is arguably futile.
In game terms, this mismatch often translates to a jarring gaming experience, such as a cakewalk against supposedly unstoppable odds, or a TPK from misuse of lethal weapons. I have had an entire campaign derailed by an attempt to rob dynamite from a construction site, and a PC commit suicide after being stopped for wielding firearms in broad daylight.
To keep the horror in horror while letting the PCs be heroes, I'll be using the following 4 levels of threat escalation to determine what resources player characters should have access to.
Note that the key to using threat levels is to communicate them clearly to players and gain their agreement that the current level for individuals or the entire party matches their roleplaying motivation, backstory, or experience.
1 Babes in the Woods
The investigators don't know the horror is real yet, and are unprepared for it.Weapons are limited to improvised or any provided by occupation (ie a Policeman or woman would have a Luck roll to see if they are carrying their service revolver, nothing more). Opponents are usually human or near-human, such as cultists or disguised serpent men. Conversely, downed PCs may be captured or wake in hospital, and should rarely be killed.
2 Fighting Back
The investigators have caught a glimpse of the true nature of the universe, and the horrors within. PCs are limited to any legal armament that they have the time and finances to secure, but still have to conceal or secure these while in public or risk investigation by the authorities. They will still be unarmed in social or official venues. Opponents are bestial or monstrous, such as Byakhee or Mi Go. One PC may be killed, but fleeing should allow others to avoid a TPK.
3 The Hunted Become The Hunters
Investigators are now seasoned and somewhat paranoid, being the object of frequent attack, and never have less than one concealed weapon on them at all times. PCs have gained access to illegal armament, and are often in emergency situations where they can be wielded openly. Opponents can be aliens or servitors of the gods themselves, such as the Wendigo, or Cthuloids. If players aren't cautious, they should be warned that deaths of one or all party members are in the cards.
4 The Nuclear Option
Investigators can have any weapon, and may even call on airstrikes or torpedoes. However, considering that they are up against the Old Ones or Outer Gods themselves, this should be effectively useless, a time-biding measure to stave off armageddon. PCs are putting themselves in mortal peril, and the possibility of deaths or even TPKs should be acknowledged by all at the table.
Note that the Keeper can adjust the level of threat to match the campaign. Call of Cthulhu games typically can start as level 1 Babe In The Woods horror one shots, or else could be level 2 investigators. However, Esoterrorists characters are created with their first supernatural meeting behind them, so usually start out at level 2 or 3.