I would advise starting small with the garden - a couple of pots of compost and buying a couple of high-production plants from the garden centre for year 1, and perhaps a small patch of potatoes. Things like tomatoes, or sweet peppers, or courgettes are all good if you have decent sized pots. "Bush" type tomatoes (varieties like "tumbling tom" and I think "Sungold" are good ones) can be grown in hanging baskets if space is an issue. Broad beans or peas or French beans can be pretty productive in a small space, and grow easily from seed (I grow dwarf French beans in window boxes, and peas up against the fence so they almost disappear there).
But only grow what you and your family will eat - not what everyone on the net says are good to grow. And preferably things that are expensive to buy versus growing (peppers, chillies, courgettes), or are difficult to find in shops (eg rainbow chard) or that taste particularly good when fresh from the garden versus days later in shops (peas, salad leaves, radishes).
Do a little this year, and maybe a little more next year, and improve the soil slowly over the years. Don't try to achieve it all at once. And build up a compost bin or heap for improving the soil - veg peelings, apple cores, tea leaves/bags, coffee grounds, etc - a little bit of citrus peel is fine, but no cooked food or anything with meat. Making your own compost cuts your costs (less need to buy it), cuts your bills (reduces bins bill) and helps improve the environment (not sending compost materials to landfill but recycling within the ecosystem to grow more good food for the family at much lower food miles).
And in terms of entertaining DCs, look at cheap or free ideas that are active. Like the family hikes mentioned. National trust type places. Nature walks or foraging walks as a family. Do some research before you go places to make the most of them - so learn about historical facts or some ecology of the area (might you find particular types of trees, or is it a good time to see tadpoles or sheep or maybe its dragonfly season....). Or to add bits of education to outings in various ways (homeschooling sites are great for this, even if you have no intention to homeschool - just to feed their imagination and stretch their interests in things). Buy things like wellie boots and waterproofs, and allow the DCs to jump in puddles and climb trees and build shelters....
Keep things that may be useful - like a button jar and a screws jar for repairs - but sometimes they can become raw materials for fun projects too.
It might seem counter-intuitive, but try, if possible, to buy good quality items, especially for yourself and DH, or that will be used for a long time by DCs, rather than cheap ones. Usually, that investment will pay off in time as they will last much longer.
With DD, I tended to get lots of cheaper items for everyday wear, as we were both out at work all day and I was also not precious if they got very muddy or covered in spag bol or paint etc, but spend a reasonable amount on good outdoor layers and a couple of key wardrobe items that got a lot of use (always including shoes in that). Cloth nappies were great, for use at home - although crèche never took them - but we still more than got our monies-worth from them and sold them on when DD was finished so got quite a lot of the money back again. And so much better for the environment too.
Another great skill with small DCs is sewing - for repairs to clothes, and being able to put together dressing up ideas much cheaper. It also helps with furnishing things at home (cushion covers can be done very cheaply and make dramatic differences to a room, or making curtains can be literally half the cost of buying them already made). Or getting things in charity shops and re-purposing them.
Learning to do things the "old fashioned" way - like hanging clothes outdoor to dry, or making stock from chicken carcasses, or using up leftovers - are all great skills for preppers and frugal people to have.