The perfect groundcover can be an elusive ideal. To do its job of defending the garden from weeds it needs to be both dense and thick, probably at least six inches. More height can substitute for density, (you can even call shrubs a groundcover of a sort,) but two to three inches is the minimum for even the most close-knit plants. And it needs to spread fast enough so buying the plants needed won't drain your wallet.
Finding this paragon of plants, especially one that suits your taste and situation, may be difficult but one solution is planting two or three plants together. For instance, heather looks wonderful as an expanse of fine texture and color but it's so wispy that weeds seem to find it a haven not a block. But heather underplanted with Ajuga 'Chocolate Chip' and plenty of moss is stable as well as beautiful.
By the way, the best moss to use as a groundcover is the kind found in lawns. Just rake some out, lightly so you don't get grass roots as well, then spread anywhere you need a mulch. It will grow and thicken up nicely but you can always lift it and spread it out again.
Another time to use several plants together is when the one you really want is deciduous. Sweet Woodruff, for instance, is an excellent groundcover for shade but dies back in winter. A shorter evergreen plant such as Speedwell (various Veronica species) will thicken up enough to take care of that problem.