We recommend starting small when creating your first home garden project. As Stephen says, "Start small, and aim for concentric circles of success." Rather than trying to plant a fully functioning vegetable garden when you're first starting out, you might be better off doing small projects first before taking on the responsibility of planting and maintaining a full vegetable garden.
Small garden projects can be just as fun as larger ones:

You can grow flowers or herbs in recycled milk
cartons...

Or plant succulents in recycled coffee tins...
Or
build DIY mini-gardens in teacups!

Not ready to plant anything yet? No problem! Why not build a super-cool bird feeder? Click here for a few DIY options to make at home with kids.
The possibilities are endless. So get creative and use your imagination. Or, better yet: brainstorm ideas with your kids and come up with project to do together. Once you've decided on the type of garden you want to plant, you'll have a better idea of what types of plants to choose.
Need a little more inspiration? This page has seven super awesome ideas for projects you can do with kids.