I love flowers and plants and I am also a busy wife and mother of 4, my solution that works for me is lots of perennials! They are so nice because you plant them once and they keep coming, over and over again!
When you buy perennials as plants they are usually a little more than annuals but over the long term you save a lot because you just buy them once and then you have them for years. Perennials can also be started from seeds which are usually close the same price as annuals. Sometimes they won't bloom the first year, so don't be too disappointed, just patiently wait til next year.
You can also often get perennials for free. As the grow they tend to get crowded and every so often they need to be thinned out in order to grow well. Also bushes like lilacs tend to send up little shoots all over that are generally mowed down. If you find somebody that has an old place you can nicely ask if they would mind if you got some starts from them. It is likely they would be more than happy to comply especially if you nicely help them thin all of theirs.
Over all Perennials have a huge variety to choose from, they come back year after year which saves you money and time and they are beautiful. That works for me!
p.s. you might find a lot of them on sale right now at stores as the planting season is basically over. It is still a fine time to plant perennials as long as you keep them well watered.
