On the nutrition front.... avoid rigidity. It's the American way to go big or go home. But when it comes to losing weight, that attitude gets most people in trouble. They attempt cut out everything then enjoy and restrict calories more than they have to and what ends up happening is a rebellion. It's human nature to crave what we restrict.
Test it out on any teenager, lol!
It sounds like you're not doing anything ridiculously rigid. But I sense a hint of dichotomous thinking where you're labeling some foods as "good" and some foods as "bad."
In reality, based your diet on lean protein, fruits and fibrous veggies. It sounds like you're doing that. But don't be afraid of other things. For instance....
I eat a lot of protein for a number of reasons. It's the most fulfilling nutrient. It has the highest thermic effect which is simply a fancy way of saying it bumps metabolic costs up slightly higher than the other nutrients when digesting. It preserves lean tissue when you're in a calorie deficit since your body will preferentially tap into the pool of amino acids in your blood stream before it does your stores of protein (muscle). That's assuming you're eating adequate amounts.
It's the centerpiece if you will. I'll take in a good 200 grams of it. Generally speaking, I tell people to shoot for 1 gram per pound of goal bodyweight. Some people think it's hard to eat this much protein, but in reality, I simply get some at each meal and I shoot for 4-6 meals per day. I'll use chicken breast, turkey breast, (ground or the actual whole breast), lean cuts of steak, lean ground beef, pork tenderloin, fish, eggs, dairy, whey protein, etc. I enjoy these foods and I sure as hell don't feel limited.
I aim for 2-4 servings of fruit per day, any fruit. I also aim for 4-6 servings of fibrous veggies per day. I go heavy on the veggies as they're extremely calorically-sparse and go a long way in filling up the old stomach, which in itself is a satiety signal. Apples are good for this too.
On top of this, I'll add a fish oil supplement.
That's my foundation. Many people think that needs to be the end of their food intake. It's natural stuff. There's little sugar besides the fruit and veggies. It's nutrient dense and calorie sparse. But in reality, for the vast majority of people... especially people who are carrying around 50+ lbs of excess fat... it's not the end.
Energy/calorie requirements are heavily dependent on body size. The larger you are, the more energy it costs to move around. The more tissue you have, fat and muscle, the more "expensive" it is to maintain your body. The more you eat, the higher the energy cost of digestion.
Stopping at the foundation will certainly lead to weight loss. The problem as I see it though is most people wouldn't be able to sustain it for very long. Some can. But what's the point in nixing foods that you enjoy, assuming you're able to control their intake when you do in fact eat them?
The foundation accounts for a portion of one's caloric needs. Generally it accounts for 50-80% of one's needs.
So adding some whole wheat grains (bread, wraps, pasta), rice, oats, etc to the mix isn't going to kill you assuming it remains within your caloric goal. Hell, I even go as far as to tell my clients to keep eating their goodies if they enjoy that stuff and have no problems with control issues... just as long as they cover their bases on the foundational side of things.
So that's a long winded response all to say be easy on yourself with regards to nutrition selection.
On the exercise front... baby steps. You're on the right track by starting with cardio. Build up volume and then work on increasing intensity. 4-6 days per week should be the goal. 20-60 minutes per session once your conditioning is up there would be nice. Once you're able, throwing in some interval training for some of the sessions would be wise too.
Strength training isn't a necessity at this point. I certainly wouldn't tell you to avoid it as it won't hurt. But in terms of bang for your buck... it's not all that. In fact, most people with a lot of weight to lose MUST loose some lean body mass in order to achieve a normal weight.
That said, nobody wants to lose muscle as, at the end of the day, what's left after the fat is gone is ultimately what will define your physique. Some folks don't eat enough protein, starve themselves, and never start strength training and wind up a lighter, still soft version of their former selves.
In your case, if you are to start now, I'd maybe do 2 days where one day is an intensity day (think 6-12 reps per set) and another day is a volume day (think 12-20 reps per set). I could get into specifics beyond that if you'd like... but this is already getting far too long.
Hope something helps here.