Plug plants are really for people who have a greenhouse, don't mind potting on a couple of times and are prepared to wait a year for the full effect.
I would imagine that you want more of an instant hit, with things that will look good all year interspersed with others giving you seasonal interest. I think you might want plants that are hard wearing with regard to the occasional ball or child falling on them without hurting themselves or the plants. Also think about whether you want to do occasional work on the plot or just low maintenance.
So you could space your plants out and throw in some annual seeds in the spaces. Calendula, California poppies, Nigella and Candytuft all grow really quickly. They can be picked by the children as this will just encourage more flowers and have really interesting seed heads. My kids called Nigella seed heads 'Fairy Carriages'. Then in the autum when they have finished you can plant bulbs in the space.
For year round interest I think Hebe is perfect. They have pink and silver leaves and interesting flowers of every colour. Very hardy and low maintenance. Instead of a fence you could plant a hebe hedge alternated with dwarf lavender. Spring and summer impact I would plant a Weigelia and Hibiscus. Weigelia is early summer, Hibiscus late summer. The flowers last for ages, unlike some shrubs which have a huge impact and then disappear in the first shower. For Autumn Spirea, Gold Flame is good and for winter Cornus Midwinter Fire. As a climber I would choose summer Jasmine and the thornless rose Banksii Lutea. Fabulous perfume for both. All of the above are low maintenance and Hardy.
Then I would have a perfumed area. lemon Mint, Ginger Mint, Chocolate Mint, Lemon Balm, Oregano and lot of differs thymes . I would plant these Either side of the path so that the perfume will be realeased as you walk on them or brush past.
If you don't like these then ornaments grasses are excellent. If you buy fairly tall ones they give a sort of secret garden feel and you can leave them over winter whenThe frost will crystallise on the seed heads and look magical, especially if you plant the Cornus Midwinter Fire in the middle of them,. Grasses I recommend are Stipa Tennuissima, Calamagrosti, Karl Foerster and pheasants tail grass Stipa Arindinacae . Piet oudolf landscapes is a great site to google.
Heathers and low growing conifers will provide evergreen ground cover and keep away the weeds, but can be a bit prickly for little hands and feet so need to be planted away from the path.