Weight lifting?

The main reason is that I can do this at home instead of joining a gym

Resistance training of some kind is important and complementary to cardio work, you don't need a gym as bodyweight resistance training can give you some good effects. Google You Are Your Own Gym for a good system, and there are some YouTube videos that you can use to support your use of the programme.

There are alternatives, but it's low cost and effective.

The more muscle you have the more efficient your body is at burning fat so if weight loss is your goal then weight traing is pretty important. Long periods of cardio though have a nasty habit of burning muscle as an energy source (that's why you don't see body builders running for miles), you'd be much better off doing HIIT training where you go all out on an exercise, recover, and repeat. This not only burns fat while you're doing it but it burns fat for a few hours after too. This is why sprinters are a lot more lean than marathon runners. I find the easiest way to do this out of the gym is to alternate sprinting and walking between street lights.

However if your not quite fit enough for this yet you may be better off doing fat burning on a treadmill first, where you keep your heart rate at its optimum fat burning zone, which is not as effective but it's a good start and won't burn muscle. To find your fat burn heart rate you take your age away from 220, and around 60% of that is the optimal level, although you can easily find a calculator by googling fat burn heart rate calculator. There's loads of stuff on HIIT training on Google too.

I know this works because I've changed over from cardio training to weight/fat burn training myself. There is a massive difference in my body now, I'm a lot more lean and not so bored in the gym now I've given up long cardio sessions. I've found that body builders are the best people to look to for weight loss advice as they have to get their body fat percentages down low without loosing their hard earned muscle.

Long periods of cardio though have a nasty habit of burning muscle as an energy source

Not really, unless you're talking about several hours worth of CV. The suggestion that 45 minutes of CV a couple of times a week will do this is nonsense.

This not only burns fat while you're doing it but it burns fat for a few hours after too.

You're talking about single figures of calories for most exercisers there.

This is why sprinters are a lot more lean than marathon runners.

That's a function of the resistance training that they do, not a function of their running.

However if your not quite fit enough for this yet you may be better off doing fat burning on a treadmill first, where you keep your heart rate at its optimum fat burning zone, which is not as effective but it's a good start and won't burn muscle.

No, the idea of Fat burning zone was demonstrated to be nonsense about 10 or more years ago

You can't really argue with results. I have less fat on my body and more lean muscle now I do HIIT/fat burning and weight training, than I did when I was doing cardio and weight training. There was a study at a Canadian university (amount others) to back this up. Body builders don't do cardio yet they have lower body fat than most others, even though they need a calorie surplus to build muscle.

Although I do admit that as long as your body has had enough food to fuel your cardio workout it will use that as an energy source before the muscle, but that will just stop the food being stored as fat and not really burn the fat you already have.

You can't really argue with results

Indeed, but I'll generally take results where the sample size isn't N=1

Personally I've taken a third off my bodyfat percentage using predominantly CV work and bodyweight resistance training. that's in the order of 30-35km of running per week with two bdyweight sessions

I have less fat on my body and more lean muscle now I do HIIT/fat burning and weight training, than I did when I was doing cardio and weight training.

So if I can paraphrase, you have seen more success by doing mixed cardio and resistance than you had doing non-specific cardio and resistance... I'd agree that any CV work does need to be in a variety of modes to get most effect, in the same way as the muscular system adapts to load, so does the CV system. As a runner I do a combination of long slow aerobic base complemented by speed interval sessions and tempo sessions. Those all have different effects on both my running performance and my composition.

Of course most runners don't only do running, resistance training reduces injury risk and help performance improvement. Some upper body strength helps with speed and stability, for example.

Body builders don't do cardio yet they have lower body fat than most others, even though they need a calorie surplus to build muscle.

Which is fine if one wishes to be a bodybuilder. Personally it's not the result that I'm after as my objectives are different. fwiw having worked with bodybuilders in the past the very restricted deit that they imposed on themselves was dull, by knocking out 1000 cals on a run it opens up lots of opportunities to eat what I want.

Although I do admit that as long as your body has had enough food to fuel your cardio workout it will use that as an energy source before the muscle, but that will just stop the food being stored as fat and not really burn the fat you already have.

Fuel is accessed in a number of different ways, but it's going to take a serious amount of effort to deplete the readily accessible.

The "muscle wastage" argument keeps coming up but it's so much of an edge case it eally doesn't apply to the vast majority of people.

Essentially, for best effect do both CV and resistance training. The two work together and unless one has very specific sports performance objectives there is little point in devisating from a mixed approach.