If you want a reliable ground cover plant choose Vinca minor / Periwinkle. Now is the time when it sets lots of blue stellar flowers. There is also a new growth of glossy leaves that cover the ground so quickly and densely that the weeds have no chance. It is grows well in sun or shade and I really don't know why is it so unappreciated.
I have it planted under my dogwood bush, along with some other plants like Liriope muscari, its grass like foliage popping out of the periwinkle sea, and Chaenomeles japonica (Japanese Quince). This Japanese Quince of mine has a low growing, almost creeping habit.
This is the periwinkle cultivar 'Aureovariegata' with golden yellow variegated leaves. On the older leaves this green - yellow contrast is not so visible as on the young ones. I am planing to purchase the one with the white flowers to light up a dark corner in the garden.
Vinca 'Gertrude Jekyll'