I just do standard stuff at the gym and plod around the rec every other day. All activity requires your core muscles - which inherently includes your back - and whilst it won't get rid of loose skin, it does protect the entire chain from head to toe and acts as an internal Playtex 18 hour girdle (remember those ads?) 24 hours a day.
10-20 minutes on the rowing machine at an easy pace but good technique would probably suffice, but I also target my upper back and leg muscles with weights on different visits. The plod round the rec is for fresh air, daylight, seeing a bit of greenery and the all important weightbearing exercise for bone density. Just by moving, you're performing multiple leg lifts and working the entire core in the process. Good running shoes are essential for that, though. A running shop can do gait analysis and advise the best shoe and fit.
As an aside, if I'm feeling bored and restless or waiting for DP to get out the bath so I can have a pee , I'll sometimes use the upstairs bannister like a barre and do ballet style stuff for a short time. Or I'll stand on a wobble board for five minutes because it's funny how hard it is (I have a strange sense of humour) and it helps ankle flexibility. Good for maintaining a low risk of falls as I get older, too. If I could be arsed with the weird booking system and massively inconvenient hours for the local pool, I'd swim as well, but that would be for pleasure, rather than any form of 'doing something healthy'.
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Regarding the PP's back pain
Some GPs are able to refer you to physio/gym rehab for back pain. DP hasn't needed that since I've shown him how to use a rowing machine and weights. I've also been a nag about posture and he's now aware of how he holds himself.
You could take a photo of yourself on timer standing up wearing shorts and a top, face on, side on and back to the camera. Ignore your face and figure, this isn't for the benefit of a framed photo, it's to look at the shape of your back and alignment of your skeleton. That would reveal your posture and if there are any elements that need work and could be contributing to your pain. Common things that contribute towards pain can be;
Poking your head forward.
Letting your shoulders roll forward. (if in doubt, tits out and proud is the correct way to hold them).
Overarching your lower back/tilting your pelvis backwards. Often combined with weakened outer leg muscles than mean you look knock kneed or your legs turn in.
Your feet collapse inwards at the ankle and the arch flattens out. Being straight on your feet affects the entire structure, as it means your knees are in the right position, which means your thighs are, your hips and pelvis are, your lower back is and it's easier to ensure your mid and upper back, shoulders, neck and head are where they are supposed to be.
A rough description could be that it looks like you're slumping into a C shape when it should be a nice curve. Might pick up one hip higher than the other or slight scoliosis whilst you're at it (DD2 has that, the first sign was having a narrower waist on one side than the other and her shoulder blades stuck out like little wings).
Of course, not all back pain is due to muscles, there are medical conditions such as inflammation that can cause it, but if the GP is happy that these aren't the case, chances are that it's lack of muscle tone causing the pain in the first place and making it more likely, along with the poor mechanics of posture, that any movements (don't lift, bend and twist at once, for example) can cause greater pain and injury.
Other things that may help, depending upon the cause include
Foam rolling and lacrosse balls. Possibly the most effective - and evil - things in the world. You know the sore muscle thing where if it's pressed on in just the right spot, it really, really hurts but feels good at the same time? That's what rollers and lacrosse balls can do for you, plus you are doing low impact bodyweight exercises to get the things into the right position. Don't roll into the lower back, but having it underneath your hips with your feet raised, knees bent, against the sofa or for more pressure, the wall, can help free off the muscles and regain the correct hip angle. The upper back can be rolled and the soft insides are the perfect width for encouraging your neck and head into an upright position rather than pushing forward.
Once you know what 'straight' feels like, you could then do leg bridges, raises, lifts and suchlike to get enough muscle strength to be able to exercise more.
Swimming. Or rather, moving around in water to regain flexibility and some strength, take the weight of poor posture/muscle weakness off your poor back, cooling down sore muscles or joints and having time when you aren't lifting, carrying or otherwise doing anything other than focusing on yourself and how good it feels.
Or, instead of some muppet like me evangelising about it on the internet, scrape together some cash and make appointments with a sports physio. They're great at seeing and explaining what's going wrong and what you can do to deal with it in a safe manner. Whilst instructors should be very able to spot and adapt things, for sports physios, that is their entire job - to identify problems and solutions. I have unfortunately seen some instructors who aren't that great, osteopaths who I wouldn't trust to adjust the central heating thermostat, never mind go within a mile of my back or neck, but I have never, ever met a physio who didn't know what they were doing.