You'll soon see that all of those will grow in Charleston. All but the New Guinea impatiens will benefit from some protection from the hot sun; petunias may languish in the hottest part of the summer but will rebound after a big haircut and some cooler temperatures.

New Guinea impatiens, portulaca, lantana, angelonia, Catharanthus roseus (called vinca), celosia, pentas, gomphrena, Profusion and
angustifolia zinnia........just to name a few!

Be sure to visit the great privately owned garden centers in Charleston and Mount Pleasant for the best ideas and selection and advice.

I lived in the Lowcountry for over twenty years. Your planting options are greatly increased, your growing season enlarged to all year color.

You might want to visit the Annuals Forum, usually much busier than this one.

I'm not in SC, but in Southeast VA. However, petunias do not do well for me at all. They just can't handle the heat, even if I give them some afternoon shade and plenty of water. They virtually always fizzle before summer is over.

I haven't tried impatiens, but vinca is similar and very tolerant of the heat.

All the flowers you listed will do just fine in Charleston. I've lived everywhere from Virginia beach, Edisto Beach, and Tampa and have had all those plants flourish.

A comment about the petunias. The farther south you live, the more leggy petunias become in the heat. One way that I've managed to have mine remain beautiful is to cut 1/3 of the plant each week. I just get in the bed or container with my shears & literally chop 1/3 of it back very hard. This keeps the plant thinking that it must expend energy on producing new flowers & not seeding over, which in return, makes them leggy looking. Don't cry. Don't fret. When I first did it I nearly burst a gasket thinking I ruined the beautiful flowers, but working 3 days new growth...one week later it was show time again.

Drive down to old town, park near the battlefield & take yourself a nice stroll through the old homes. Many are gated, but every outside they'll area will be nicely landscaped. Make sure to take a high-quality camera and snap pictures of what you enjoy, so you can cross reference it.

And I have to give a little plug for the plantation homes going from Edisto to Walterboro & the beautiful gardens they have. Many open up for garden tours as well. Perhaps your local extension can help you with dates.