Pretty much any plant with a spreading, creeping habit can be used as a groundcover. There is a huge difference in appearance, drought tolerance and growth habit between creeping thymes and shasta daisies - you need to pin down the look you want first THEN make your choices.

IME, shastas in full sun and relatively poor soil will be more upright than those that receive more coddled conditions. Yes, they are drought tolerant, but would be happier and look fresher with periodic irrigation. Rudbeckia (black-eyed Susan) spreads or colonizes faster than do shastas, but offers a yellow flower rather than white. Both are herbaceous perennials and will die back in winter, leaving a basal rosette of foliage present in mild climates. And they will both need to be groomed, removing old flower stalks, otherwise they can look quite messy in time.

Creeping thyme is VERY low growing - generally no more than an inch or two at the very most - is extremely drought tolerant when established and can spread quite rapidly once established. It will bloom in shades of pinks, purple or white depending on selection. It can also take light foot traffic, which the daisies cannot.

Another choice for a middle height, drought tolerant suggestion are sedums and stone crops. While the growth habit of taller sedums is less "spready" than some other choices, they divide readily, so multiplying your plants to increase coverage is very easily and quickly accomplished. Lower growing stonecrops spread rapidly on their own, but they, like the thyme, will be quite low to the ground and may not be visible behind the taller bearded iris.