Put some bat boxes up,and bird boxes, hedgehog boxes, couple of paving slabs up on small blocks, to make habitat for snakes(a good compost heap for winter accommodation),a rockery with lots of pipe and gaps, toads and frogs, put in a pond with proper grid, to encourage their natural predators, put them on the bird table,
Give the children 50p for every hundred they collect, feed to the birds, or give to a fisherman.
you can put bug traps in the lawn but you risk killing helpful critters such as lizards,
Just make your garden the best place for all the predators to live, then all the neighbour hood predators will move to your garden, and will eat anything bad.
If you start to spray, you will never get a balance in your garden, and you will always be fighting them,
When I get a pest, I have a really good look at why the predators are not there, I try to provide 5 star accommodation for my killing guests, then they do all the work for me, once they move in they stay forever as long as the service is up to scratch.