You've gotten some good advice. I'll make a couple suggestions. First on cardio and then on strength training.
I'd echo the cardio, as long as you also maintain the strength training (cardio alone can cause your resting metabolism to fall, but studies have shown the two together maintain or raise resting metabolism, so that your exercise is leading to more calories burnt without the downside of burning fewer calories when you aren't exercising).
Quality cardio gets your body able to burn fat to a greater extent when you exercise. Get some steady state cardio for at least a few weeks to get your body used to it, but then add some interval sprinting for maximum metabolic impact.
Like everything else, what is intense for you will depend on your condition. It may just be walking at a faster rate, or a slow jog. The key will be to bump your heart rate up above the aerobic stage so that you start to build some lactic acid, followed by a recovery stage to allow your heart rate to come back down to normal.
The impact is that your metabolism will stay higher longer after you stop exercising than low-intensity steady-state cardio, as your body recovers from the more intense training.
Here are a couple examples of intervals that tax several of your energy production systems. Mix them up and improvise, as this will ensure the best improvements in conditioning and keep your cardio more interesting. Interval sessions should be shorter than your regular sessions in time.
Type 1 (pushes your aerobic threshold): after warming up & about 5-10 minutes of normal aerobic work, do a couple sets of 3-5 minutes at about 80% maximum heart rate (just at the point you can no longer carry on a conversation while you exercise if you don't use a heartrate monitor), followed by about half that at a slower than normal pace to allow your heart rate to recover.
Start with a couple sets, and build up slowly by making the sets longer (i.e., start at 3:00/1:30, then slowly build to 5:00/2:30), &/or adding more sets. Finish with a few minutes of normal low-intensity cardio, and then a cool-down period.
Type 2 (pushes your ability to work the lactic-acid producing anaerobic system that is typical of sports like tennis or basketball- a bit more intense on the sprint and the recovery phase, but longer recovery): again after warming up & about 5-10 minutes of normal aerobic work, do 1-4 sets of 4 repetitions of 30sec. - 1:00 at about 85% maximum heart rate (once you get used to what your pace is in type 1, just push it a bit more so that have a bit more difficulty carrying on a conversation while exercising), and twice as long in a recovery phase that is close to your normal cardio pace.
You are trying to get your body efficient at clearing lactic acid under a normal cardio load. Again start with 1 to 2 sets at 0:30 sprint / 1:00 recovery, and gradually over time lengthen your sprint/recovery to 1:00/2:00, and your number of sets.
Finish with a few minutes of regular cardio and then cool down. I usually add an extra minute or two of regular cardio between sets to ensure that my heart rate has recovered and I'm ready for the next set.
Type 3 (pushes your explosive power, focusing on the creatine-ATP energy system, which tends to be activated for the first 10 seconds or so of hard work). Similar on warm-up & a few minutes of regular cardio, but here the sprints will be shorter and harder, and the recovery slower and longer.
I do sets of 10 repetitions of about 10-20 seconds near all out, followed by three times the sprint in very slow recovery (so 30-60 seconds). Start with a couple sets, and gradually build up to about 4-6. Like the others, add a few minutes of regular cardio between sets, at the end, and finish with a cool down.
Add add type 3 sprints after going at least several weeks (more probably preferable) of doing intervals, as it is the hardest and not for someone in poor cardio condition.
Start with doing one sprint-interval session a week, and then as your cardio fitness improves consider adding a second session. Remember, though, that you need to give your body time to recover from these sessions, so doing too many a week when you are doing strength training and other lower intensity cardio may be counter productive.
I usually make my first training session of the week sprint-interval (i.e., the day following my rest day) so that it doesn't impact my recovery from strength training days.
I usually do a moderate intensity cardio day which is just below the being able to carry on a conversation (75-80% MHR), and a long, low-intensity session (65-70% MHR, for 50-75 min.) to burn fat (a greater portion of the energy comes from fat than carbs at low intensity, & although the overall caloric burn rate is lower than higher intensity the ability to go substantially longer more than makes up for this).
Turning to strength training, I'd echo the comments on trying some of the compound exercises with little or no weight. Read up on how to properly and safely squat, deadlift, lunges, bench press, military press, rows, etc., and work on the form.
These stimulate the central nervous system to cause systemic muscle/strength development, hit the biggest muscles & more muscles at the same time & will burn the most calories, and are efficient as they work multiple muscle groups at the same time.
It is very difficult to develop proper, safe form under a difficult load, so you start with next to nothing. For instance, do squats with just the barbell. If this is too tough on your back, start with a broom stick. Concentrate on getting on doing the exercise with perfect form. Then, each session, add a small amount of weight.
Even if it feels like you could lift a lot more, resist the urge as you train yourself to do the exercise with proper form, and progressively add weight. I make squats the center piece of my strength program, doing them each session. I do deadlifts, bench, military press, seated rowing, chin-ups/pull-ups, and dips on an every-other session basis. That is pretty much it.
It is based on Mark Rippetoe's beginning strength training program using 5 sets of 5 reps for the squats, bench, rows, and military; 1 set of 5 for the brutal deadlifts; and a couple sets of 8-10 for the dips and chins. Your arms get plenty of work. If you can't do dips or chins, try doing just the negatives. Use a chair or a step-stool to assist in the lift, then try to lower yourself in a controlled fashion unassisted. As your weight drops, & your strength develops, you'll need the chair less.
The only other thing I do are some balance, low-back, and shoulder girdle support pre-hab work at the end of my strength sessions. This might be good for you, especially the lower back. I'm trying to remember where I saw the horse exercise, but look for articles by John Davies.
He has some good shoulder girdle, low-back, pre-hab exercises that I've incorporated to help strengthen the small weak support muscles that allow me to do the regular lifts.
Good luck, don't get discouraged if you don't make the initial progress you hoped or fall off the wagon (we all do- the difference is that some don't let that stop us). You are doing something to eat more healthily and to exercise, and that is the biggest step. It probably took you years to get to the state you are in, with some brief times where you halted your decline/expansion.
It will take time to get there in a healthy manner that you can sustain as a lifestyle, and you will probably face some cheating and set backs along the way. Just keep going, keep trying to learn how to do all this more effectively, add to what you are doing as you can and find things that challenge you and keep it interesting, reward yourself for sticking to it as well as making progress, don't set your hopes on some miracle supplement to substitute for consistency and work, drink lots of water, take your fish oil supplements, eat 6 smaller meals rather than 3 bigger meals (at least for a while count calories as studies have shown we tend to underestimate our caloric input), & try to do something that makes you laugh every day (i.e., stress makes you store fat- so lower your stress level so your body can switch out of fat-storing survival mode).