I just recently worked back into shape and so I'll tell you what I've done. I lost about 45 lbs in less than three months. Not that losing weight rapidly was my goal, it just happened to be the result. I don't think it matters that you lose it fast, you need to feel healthy while doing it.
I started off following the Maffetone two week test:
https://philmaffetone.com/2-week-test/
I found that I had the symptoms he describes of CI. After the two weeks I slowly introduced some carbs, only whole fruit type not any processed. Currently my daily diet is usually this:
Breakfast: Scrambled egg (Costco) recipe from The Four Hour Body book, I only use salt, pepper and parsley for spices. Add salsa and quacamole. Coffee (Aero Press)
Lunch: Chicken breast (Organic three pack Costco) pan fried with olive oil and butter. Usually spice with garlic salt, greek spices or barbecue type spices. Microwave in a small pyrex bowl the normandy vegetables (Costco) and add butter, salt and pepper. I'll also do steak and fish. Usually I'll cook the steak in a Sous Vide as I like the way it turns out and it's easier for me to achieve a great steak.
Dinner: Green smoothie in a vitamix: Water, orange, banana, honey, vanilla extract, spinach, frozen pineapple.
Snacks and to deal with the carb demons: Raw unsalted cashews (Costco), cheese (sliced variety pack from Costco), Coffee (Aeropress both hot and iced / cold press method).
The coffee has helped me kick the soda addiction, along with carrying an insulated water bottle (zojirushi)
I usually do a free day on Saturdays, but not always. Sometimes I'll skip it especially if I had a couple of cheats during the week or my weight seems to creep up.
Workouts:
I workout six times a week, I use the maffetone fat burning cardio training method three times a week for 30-40 minutes each with a heart rate monitor (works like magic for me, I don't have horrible cravings as I've had on other kinds of workout plans):
https://philmaffetone.com/180-formula/
The other three days a week I do Starting Strength with the iphone app. I've found the app to be invaluable in following it on my own. I have read most of the book and watched his DVD. I found starting out slow and really working on form helped a ton.
I feel a thousand times better on this program and it's worked well for me. I was at a 32 BMI and brought it down to 25. I was about 250 lbs and now stay close to 200. Everyone comments on how different I look and I've noticed much better muscle definition and strength. I'm not trying to do muscle building or any extreme stuff, I just want to be fit and feel great. I've achieved that goal and with fairly minimal effort. I spend a lot less on food as I rarely eat out and I find it takes less time to make it myself.
It took a couple of hard weeks to change habits and get with the program. Once the habits were in place it's been very easy. I naturally look for low carb and food that is close to the diet I'm trying to stay with. Whether it's called slow carb, or paleo or whatever doesn't really matter. Just figure out which foods work for maintaining your healthy weight and fitness level.
I think remembering how awful I felt about 100% of the time helps me to stay motivated with my diet and exercise. I think you really need both to make it work. If you focus on one and neglect the other you are likely sabotaging your effort. You could maybe get away with only focusing on diet, but it depends on your normal activity level. Given my sedentary job I need the workouts.