For sunny spots, the reliable performers are lantana, geraniums, petunias, salvia, and compact ornamental grasses. In shade, switch to coleus, ferns, begonias, hostas, and impatiens. For structure that lasts all year, dwarf boxwood and small conifers handle pots well, and most herbs (rosemary, thyme, basil) are happy in containers by a kitchen door.
Designers often build a container with the "thriller, filler, spiller" rule: one tall focal plant, a few mid-height plants around it, and something trailing over the rim. It works because it gives a pot height, fullness, and motion in one shot.
Two practical notes: pots dry out much faster than beds, so expect daily watering in summer heat, and a potted plant effectively lives one to two hardiness zones colder than the same plant in the ground. To try container and bed combinations on your actual patio before buying, OutdoorBrite works from a single photo.