Aka Ivy Leaved Toadflax which is the more usual common name over here.

Landscape roses are considered groundcover roses. They are low growing shrub roses (typically not exceeding 3') that spread much wider than they grow tall. Drift, Knock Out, Flower Carpet are all readily available landscape groundcover-type roses. It is not a defined category, but the roses are bred specifically for these attributes. They also tend to be very free flowering and low maintenance compared to other rose types. The issue with most groundcover clematis is that they behave exactly as do their vining cousins....except they don't vine :-) So for the most part, they are not tidy little clumping things but large rambling plants that can easily grow several meters a season. Combining the two - the wide, sprawling landscape roses and the long, rambling clematis - may not be as simple as it sounds without very careful cultivar selections.

We put plastic over our ground cover to try and kill it and then mulch on top. Don't want to use pesticides because we want to replant in the garden.... Well the ground cover survived and grew through the plastic. It will not die. I rip it alk out every year and it comes back no matter what. It's a fight that never ends. It chokes out my other plants. This year I'm planning on launching a full attack.

Trail mulch if you can find it. I get it from my county compost site for $10 a yard and it consists of much larger wood chips and sticks than will be found at a supply center. The county also uses this on their walking trails through nature preserves, so your application is exactly what these chipped are used for. Because of the sizes trail mulch is less prone to washing away, but It isn't pretty, just functional and economical. I also get wood chips deliver through a place called chipdrop for free. I get more than I want because you get a truck load, or loads, so check to see if chipdrop works in your area and request an order of what you want. My neighbor and I received over 20 cords of free hard wood logs delivered through chipdrop for firewood two years along and about 25 yards of chips. Another free source are tree cutting companies. Last fall I asked a tree company if they wanted to dump there chips on my land and they jumped on it and ended up with 4 truck loads. None of these chip sources are finely shredded chips you'd buy in bags at the store, and not the best for nice landscaping but for walking paths they rock. The last free or low cost option is repurposed decking boards found free on craigslist or where ever. Cut the deck boards into the width of your paths, drill two holes on each side and weave a rot and UV resistant rope through the holes. They can also be rolled up, moved, and finally trashed when they rot out. The last not so great option is old used artificial Turf. It's not so great because I rarely see it for free, but usually can find it for sale for more than I'm willing to pay.