Does anyone have a good strategy for controlling weeds in strawberries?

I would like to plant some alpine or coastal strawberries as a groundcover in beds along with other native plants. The beds are right in front of our house so I'd like to keep them tidy! I thought about trying landscape fabric and burying it with mulch. Would they spread into a true groundcover, though, or would the landscape fabric prevent new plants from forming on the runners? I don't think alpines put out many runners, but I believe coastal strawberries do.

Anyone have experience with this? I would sure appreciate any tips. Thank you in advance!