Flowers and vegetables require weeding, feeding and watering. I wouldn't call them low maintenance. A few tall shrubs are probably as low maintenance as you are going to achieve. Even established gardens had to be watered when first planted and flowers need constant watering in our hot dry summers. Think of the climate as you make your choices. It's also soil dependent. Test your soil, check the path of the sun, things like wind and then do some reading up on smart choices. Your local garden centre could probably advise you better. I would plant for structure first i.e. the tall items and then you can fill in with appropriate smaller plants. Do you have a water butt? You may be able to install one next to the house or wherever your downpipes are. This would help with summer watering.

What aspect are we talking about here? That will have a big impact on choice of plants. A climbing hydrangea on a shady section of fence could be a good option as they are self-clinging so won't need any intervention from yourself, and basically just look after themselves as long as you keep it well watered as it is getting established. Re fruit and veg in the raised beds you've built, they don't look very wide for vegetable growing. Not sure how much in the way of veg you'd get in there (though you could grow tomatoes in the summer months), but a fan-trained fruit tree on a sunny section could work well. Fruit bushes such as gooseberry and blackcurrant are also very low-maintenance, just requiring a winter prune. A thornless blackberry could be trained against the fence, which again is fairly low maintenance. You could grow strawberries under the larger fruit bushes. They are fairly tolerant of various light levels. And don't forget herbs. Rosemary and sage are very low maintenance, and thyme and oregano will spread and provide ground cover.

For privacy screening, NON-INVASIVE bamboo could work as they grow quickly and again are low maintenance as long as you give them lots of water. I'm not sure I'd ever dare plant out a bamboo, though, having seen the havoc they have wrecked in some gardens around here. We grew massive ones in half-barrel containers in our old house, and they provided lots of screening and they give good season-round structural interest.

Another against the fence idea could be honeysuckle. They grow quickly and spread, some are more vigorous than others. You would have to tie it in, though, and keep watered, but they give amazing fragrance when in flower.

Re the hanging basket, you can't keep plants in a basket longterm without repotting and a certain level of care. There are a myriad of trailing plants such as petunias, fuschias etc available in the summer as plugs that will grow rapidly and provide a spectacular show of colour. They will need replacing in late autumn however, so if you want to keep it as fuss-free as possible it might be a better idea to go for year-round foliage plants, such as this collection:

https://www.jparkers.co.uk/6-evergreen-foliage-plants-1008956c?gad_source=1&gclid=CjwKCAiAnpy9BhAkEiwA-P8N4hcY-76FstBb-uFzFfhv--8O9yqEDqsY7o3-nKkHZn9QjPIUD3xHShoCXXkQAvD_BwE

I think you might just have to put up with the swing set as a blight on the view for a couple of years more! By the time you had grown a useful screen around it, hopefully it would be "moving on" anyway. We've had a hideous trampoline in our garden for a few years now, and I've stopped seeing it. I had to just accept that if I wanted the children to be in the garden and enjoying it too, I was going to have to compromise on aesthetics (for now...)!!

Lots of ideas for plants from the Houzzers but I’m thinking if you have a young family you may not have as much time for gardening as you’d like so something to bear in mind. I’d also think about the sunniest spots in the garden and keep those for seating whilst the shadier areas will be better for plants. We have recently taken down a trampoline after 15 years only to realise it was hogging the sunniest, most sheltered spot in the whole garden!