I should add a #4 to this list: I have a bunch of Lilly-of-the-Valley that I could transplant from my backyard to the front. I'm guessing containment of those would be similar to the Ajuga and the Pachy.

When I lived in Denver I bought steel edging when I did design build, but its scarce in NC and that contained the invasive groudcovers. You just have to learn how to trim 2-3 times a year. I must prune back the euonymous and cotoneaster at least twice a year because it covers the walkway.

Here is a link that might be useful: Propagating Perennials

The steel edging is desirable, but expensive. With those ground covers I mentioned, would I be better off utilizing a border or edging material that is wider at the surface, or deeper when placed in the ground? Would a material like large rocks or bricks work best, or would the stolons/rhizomes just work their way under around or over them?

I moved into a house with nothing but invasive groundcovers in the beds edged with black plastic edging. The groundcovers do creep underneath the edging if they are not pulled out before getting too close to the edging. I had it invading the lawn. Once under control I just watch the edges and don't let things get too close.

I have all three. You just need to weed eat the vinca; it will climb over the edging. #2 would be easy to contain with or without border; it moves slowly. It pulls up easily or use a hoe. #3 has moved slowly in my bed; it would contain with border. In three years it still hasn't covered a 4' X 4' area. I only started with a few plants.The more you have the faster it spreads. That makes sense! Dugh