Are you looking to do a specific low carb diet? Have you seen a low carb diet that interests you?
Many of us find we lose better doing low carb then just calorie counting. I know it works very well for me. I currently do Atkins because I like how the diet is structured. I eat 20 net carbs a day (carbs - fiber content in food).
Most low carb diets consist of lots of meat and veggies and depending on the diet maybe some cheese or some dairy products as well. A few of them are meant to be high fat as well so your using things like olive oil and real butter (like with Atkins). Your questions are too broad for me to give you any specific advice. I would pick a diet and read up on it and be sure you can follow through first.
Just remember, fat doesn't make you fat
Healthy fats are great for you!