Firstly, congratulations on getting a garden- it can become a dangerous addiction and lifelong passion if you’re not careful 
I’d advise keeping it simple and starting small in your first year, else it can get overwhelming and off putting quite quickly.
For spring next year plant bulbs this October and November: daffodils, iris, crocus and tulips- easy and you just leave them underground.
For easy colour and things the children will love this year plant sunflowers and cornflowers - both doable straight in the ground from seed. Though you sow these later in the year when the soil has warmed up.
Gladiolus corms are also great (plant deep) for a beautiful spike of colourful flowers.
In the spring I’d buy geraniums from a garden centre and plant in pots or a border for instant colour. Whether you do other “bedding” plants like begonias or pansies is up to you.
I’d get a cheap copy of an RHS introduction to gardening book online- they’re simple and tell you what to plant when. Your local library will also have loads of gardening books.
In pots you can sow parsley, radishes, lettuces- just space lettuce seeds out of you don’t want to have to repot them later in bigger pots.
Do cress on the window ledge in the kitchen.
Tomatoes need sowing in soil compost in small pots and putting on a warm window ledge. Then when they’re a few inches high you need to move them in to bigger pots, then you put them outside only when the last frost has gone. To stop them being shocked put them in their pots on the back step every day for a week, bringing them back in at night. As it’s your first year I’d advise buying tomato plants from garden centres in spring.
Sweet peas (flowers, not edible) look lovely in pots- sew now for starting indoors or outside in large pots in spring- you’ll need bamboo stakes for them to climb up.
Cosmos are another lovely flower to direct sew in the border in a few months.
Dwarf (edible) pea varieties are great in flower pots too- stake as above. Your children will love picking and eating them straight from the pods.
Buy strawberry plants in spring to plant in pots. They send out “runners” in autumn which you can use to make new plants from.
Be wary of snails and slugs. Pellets are banned now and a danger to pets and children, so just go out of an evening and dispose of as you see fit- otherwise you’ll get upset if they eat everything.
Lastly- good luck and enjoy it! Don’t despair if you have setbacks- that’s normal with gardening. It’s all trial and error, and you’ll get there.
Be wary also of cats sitting on flower pots 
Good luck OP!