I converted almost 15 years ago to a hybrid diet. I started with the idea of Paleo and tweaked it to cut carbs and add fat. I say converted because it needs to be a life style change and in order to stick with it you need to feel free and have options. I have lost and kept off over 40 pounds (with a little gain back for a few years there but I'm back on message).
Here is what I do:
Practice "net carbs"
Avoid starchy veggies
No sweet fruits like bananas, apples etc
Early I target 20 grams of carbs a day
Buy keto stix to monitor your ketones, an indicator that you are in ketosis and burning fat as your primary fuel source. I target moderate levels, if they go too high it's bad for me. Stay that way for a few months adjusting carbs to maintain moderate ketone levels and the weight will melt away.
Fat intake is important for this to work, perfect for me because I love cheese and meat ( remember I said modified Paleo). Plenty of eggs, bacon, beef, pork, dark chicken meat etc.
For rice substitute look to califlower, for potato's substitute look to califlower, cabbage is your best friend. Can't get enough leafy greens many ways, fried with onion and bacon is awesome or in a salad (with cheese, meat and full fat dressing). Stir fry is a great one.
It's best to make everything but if you buy stuff READ labels.
Last but not least, at my last physical my HDL was 88 and triglycerides 54, TTL 188. I don't worry about the fat, I do eat nuts daily. It works, even knocked 2 points off my a1c. Talk to your doctor. I have lots of recipes if you want some ideas but I think I tossed alot you way, good luck!