Let's be clear up front - I have no horticultural training whatsoever! My feelings about the garden are based entirely on my experience as an 'undergarderner' (he who does the grunt work) for 38 years. I'm also a very slow learner, because it's only been the last 2 or 3 years that I finally began to think I am understanding how some of these plants behave. Here are three beautiful flowers that I recommend you either do not have in your garden, or control very carefully!
There is a bit of philosophy behind your choice of managing these flowers. At one extreme is a garden of nicely separated plants, with substantial areas of bare mulch in between. At the other is a chaotic mixture of crowded plants all mixed together. 'Volunteers', plants that come up from seeds on their own, help create this mix, referred to often as an 'English Cottage Garden'. I try hard to find a balance someplace in the middle, but you need to choose your own balance, from being ruthless to being quite slack about allowing these 'volunteers' to grow.