Greetings, comrades. So to cut the story short, my physical state is absolute junk and it's about time to do something about it. I am overweight and lose breath after going up s flight or two of stairs, my back hurts almost daily and lifting things heavier than a backpack is stating to feel hard. All the doctors say I require exercise to resolve most issues. However, due to long commute and a few other issues, I can't really visit gym on a regular basis (plus it's not cheap). So what can I do from home to stop being a useless blob of blubber? For reference, I have a set of dumbbells, but using them hurts tendons in my arms more than it seems to affect the muscles.
I am seeking advice from the comrades
Definitely look into bodyweight programs. Freeletics app has like a million programs with all kinds of difficulties, goals, etc. They're generally similar to what @CjkOvPDwQw recommended. Not sure how monetized it is nowadays, but it used to be pretty decent. Depending on how overweight you are some of the exercises eg squats might be too taxing on your joints. I'd say try them out and if you can't do them with decent form or they're painful for you, don't worry about it and skip them for now. Just do what feels comfortable and healthy for you, as long as you do something regularly and it gets your heartrate up.
Once you've built up your work capacity, got your tendons and joints used to stress again, you can look into real calisthenics if you want to gain strength and build muscle too.
But, I'd say, you should probably also take a good look at nutrition. They say "You can't outtrain a bad diet" for a reason. Working out is always better than not working out, but limiting calories even moderately would probably be the single most effective thing you could do right now. Limiting calories even a bit and increasing workload would be even better and should yield good results in no time.