One man's weed is another man's flower

We just bought a house. Holy cow how did that happen!? I went from living in a 450 sq foot one bedroom apartment above a garage to a house. A house with a garden and neighbors who bring you cookies and say hi as you park your car.

Needless to say I've never had my own garden before. Sure I helped my dad plant and water our family garden growing up, in England. Let's face it I wasn't really much help to him other than staying out of trouble. Here we are faced with the task of taking care of a [to me] ginormous backyard and a front yard to boot! What the heck people, wasn't one garden enough? The funny part is that the front yard is mainly rocks with bedding plants in small areas - or well it's supposed to be. It seems the lining of the rock part isn't doing it's job and as of May we now have a weed take over! Or so my neighbor tells me, because [between you and I] I actually had no idea how to identify which plants were weeds and which we were meant to keep. In fact I had transplanted a couple of these pretty flowers [weeds] into the flower beds before our neighbor kindly pointed out that "those will take over the entire area and choke out the other plants". Shoot.

Fast forward to the end of the month and these beautiful weeds are taking over. Driving me up the wall with their tenacity to infiltrate every part of the garden. How was I to now that those pretty flowers would be so invasive! Mint - that yummy leaf that adorns my summer mojitos - a giant pain. You sneeze and it's traveled over half your garden. Why can't weeds make it easier for you to identify - by having some kind of pungent smell or spiky unattractive foliage?!! I used to joke about who was it who decided which plants were weeds ? Arguing that "they have such pretty flowers, shouldn't we commend these invasive weeds on their hardiness their evolution?" Now I realize it was probably another frustrated new home owner just like me.

Any gardening tips please feel free to share.