Many people starting out go by the rule of 5g carbs per 100g. I totally empathise with you about fearing the fat. I slowly reduced my carb and slowly increased my healthy fats until I got to a comfortable level (which may be different for everyone). Don’t overdo the fat, we want to be using our bodies fat stores, but we do need to eat enough to keep us full and keep the carbs away. So eat healthy fat until full, eat meals until no longer hungry, and remove processed food from your diet and you almost become low carb by default.
There is extensive evidence for the benefit of the Mediterranean style low carb diet, including cutting your risk of heart disease and diabetes. It has even been found to reduce risk the risk of breast cancer, compared with those on a low-fat diet. Consuming extra virgin olive oil (the fresh squeezed juice of olives) seems to be particularly beneficial when it comes to cancer, perhaps because it contains compounds such as polyphenols which are known to be anti-inflammatory.
Use fat as a lever. We’ve been taught to fear fat, but don’t! Both keto and low carb are high fat diets. Fat is our source of energy as well as satiety. The key to understand, though, is that fat is a lever on a low carb or keto diet. Carbs and protein stay constant, and fat is the one you increase or decrease (push the lever up or down) to gain or lose weight, respectively. So if your goal is weight loss, eat enough fat to be satisfied, but there’s no need to “get your fats in” once you’re satisfied.