I'm busy all the time. Whats a really simple home workout I can do? Burpees? Squat jumps and pushups? I run when I have time.
Running "when you have time" is not enough. If you want to stay in shape, and I'm not talking about "muscular physique" but just good shape, you MUST do cardio and eat LESS. There are no exceptions, and no alternatives. In fact, if you have very limited time, it's better to just do cardio and nothing else. That would be much better than lifting weights and not doing cardio.
Again, since you said you have limited time, assuming you will do INTENSIVE cardio at least 30 minutes 4 days a week (as in coming back dog tired, shirt soaking wet) you can just limit yourself to two exercises. Pushups and pullups.
Really, there's no need for you to concern yourself with anything else. With limited time, it's better to really focus on two exercises than to spread out into many different ones. But when you do pushups and pullups, we are not talking "just do 3 sets of 10-12 pushups and you are done...". We are talking 10 sets of 8 pushups and 10 sets of 8 pullups on alternating days to start with, and increasing the number of reps to 10 per set. When you can do a good, solid 10-15 pullups, and 50 pushups in ONE set, going all the way up and all the way down, slowly, with good form, and absolutely no struggling on the way up, I'd say you're doing quite well. At least I'd say that about myself if I could do it. ; )
Off course if you're real skinny, you can just throw my advice about cardio out the window. But I'm assuming this is not the case.