Good advice there, stone. But don't forget that some things can be invasive in warmer zones and not at all in colder. My daughter's zone 6-ish garden in Salt Lake City had a big problem with invasive vinca coming through the fence from a neighbor's yard. We labored each year to get rid of it.
Then I saw it growing beautifully, in a nice controlled way just a little bit higher up the mountain (say, one zone colder) in another friend's yard. Our friend has had it for years and no problems with it taking over.
We now plant the variegated form at my daughter's house and it also is quite controllable. So, I'm just sayin' that an invasive in one area can be a great garden plant or groundcover in another.
Even the same zone in different parts of the country have different criteria for invasives eg. in zone 8 in British Columbia where I grew up, periwinkle is used widely and much appreciated as a lovely groundcover for under trees. I'd suspect that the long, chilly, gloomy and damp winters keep it in check.
