If you're eating low carb to prevent cancer then you.ll probably need to eat a ketogenic diet, i.e. no more than 20g per day. So that's 5% carbs, 15-30% protein and the rest from fat.
If you want to add berries for health then they should be your main source of carbs. Total full fat yoghurt is a good low carb choice, you can further reduce the carb content by adding double cream or full fat creme fraiche. You may need to consider not having too much dairy, maybe only at one meal per day; apart from butter which is unlimited.
I would continue to use MFP until you get into the swing of things. It isn't 100% accurate but it will give you a good idea of what works for you.
If you like eggs then they are a great low carb option and very quick to prepare. Eggs mashed with butter, scrambled eggs with loads of butter, omelette fried in butter... are you seeing a theme here?!
A good meal plan would be:
Breakfast: 50g berries with 150g full fat yoghurt and a splash of double cream or creme fraiche.
Snack: pork scratchings - the Awfully Posh ones from Waitrose (or Amazon) don't have nasty additives in, or celery sticks, or a hard boiled egg, or a small portion (1-2oz) of almonds/macademias/brazils, or a couple of squares of dark chocolate.
Lunch: an eggs dish OR salad leaves with oil and vinegar dressing and tuna mayo or leftover cooked meat or ham or a chop/steak. I like rocket, watercress, baby spinach as they are much more nutritious than lettuce which is basically crunchy water! Cucumber and celery are low carb if you want a bit more texture to your salad. Cherry tomatoes are carby but you could have two or three sliced up thinly to make them stretch further.
Dinner: Fish or meat (go for fattier cuts such as pork chops, sirloin, chicken thighs) with vegetables either roasted, cooked in butter, or steamed/boiled then with melted butter poured over. Mushrooms, celery (delicious braised), kale, spinach, broccoli and courgettes are all so low carb you can basically eat as much as you want without worrying about the carb count. Celeriac, leek and cauliflower are slightly higher in carbs but still good choices.
If you drink a lot of tea or coffee then you can cut carbs there by using almond milk. The fresh versions are less nutty in flavour than the UHT versions.
Make sure you are drinking a lot of water. At least two litres a day including tea, coffee, herbal tea, etc.
Disclaimer - I am not a doctor, merely an informed observer so do your own research on what is best for your particular concern. I do recommend joining a forum or support group as there are plenty of other people in the same boat and they will be able to advise you.
Good luck!