Welcome to the South! You'll love being able to start your serious gardening in March, and not having a real killing frost until nearly Thanksgiving. (Our hot humid summers may take some getting used to, though. :)

My favorites, in no particular order:
loropetalums
camellias
crape myrtle
daylilies
hydrangeas, especially Endless Summer and Blushing Bride
Rabbiteye blueberries
Celeste Figs
Wait till you taste Muscadines!
Salvias: Black and Blue (perennial here), Mystic Spires, farinacea
Bulbs: Rain lilies (zephyranthes), Crinums (these alone are worth moving south for), Narcissus, Grand Primo, Campernelle Daffodils, Trevithian Daffodils, Cruentas Byzantine Glads

Be sure to get a copy of The Southern Living Garden Book. It will be indispensable. Scott Ogden's Garden Bulbs for the South is a good one too. Enjoy

Favorite sun perennials:
Rain lilies
echinacea (coneflowers) especially the newer ones
salvias - 'black and blue','coral nymph', 'lady in red' (hummingbirds love them)
daylilies
daisy
black-eyed susan
clematis (lovely draping over a wall)
hardy orchid

favorite shade perennials:
hosta
coral bells (heuchera)
foam flower (tiarella)
all the ferns - autumn, southern wood, sensitive, japanese painted, lady
lenton rose-love love love
phlox divaracata
toad liliy
wild ginger

i hope you enjoy gardening in the south!

Thank you for all your picks. I can't wait to get started.

Thanks for posting this, Stephanie - I too am new to SC, and was wondering what might work well here.

I like
1. Daylillies
2. Coneflowers
3. coreopsis
4. Hosta
5. Balloon flower
6. Pincushion flower
7. Iris
8. Sedum Autumn Joy
9. Arborvitae fern

10. guara
11. Shasta daisy

Must have southern tree/shrubs
1. Southern Magnolia 'Little Gem'
2. Azalea
3. Camelia
4. Osmanthus frangrans
5. Knockout roses
6. Dogwood
7. Viburnum carlesii
8. Hibiscus
9. Vitex

10. Carolina silverbell

Welcome to SC, Stephanie. Where is it exactly are you relocating to? I notice you have a zone 8/9 listed which makes me think you may be near Charleston. Me too! If so, Zone 8/9 is a unique little gardening area. You'll enjoy gardening here more if you don't try to recreate what you are familiar with but embrace what is unique to the area. Instead of lilacs, peonies, and hostas think palms, camellias, cycads, aroids, even some citrus.

My favorites by category:

Perennial:

Katie Ruellia (NOT the tall ones which are invasive)
Cuphea micropetela (giant cigar plant)
Brugmansia (comes back from the root every year)
"Bright Eyes" Phlox(not all the tall ones thrive here)
Plumbago auriculata (marginally hardy)
rehmannia glutinosa (Chinese foxglove)
Indigo Spires salvia

Evergreen Shrubs:

Banana shrub
Pittosporum (there is a tall and a dwarf variety)
Gardenias
Cleyera
Lorapetalum

Roses:

Knockouts
Belinda's Dream
(most other roses are a pain in the heinie around here)

Summer Annuals:

Blue Daze or evolvulus glomeratus
Profusion series zinnias
pentas
cosmos (especially sturdy are the orange, red, yellow ones)
Torenia Summer Wave series
Ceratotheca tribloba (african foxglove)

Tropicals that may work:

Satsuma tangerines
Meyer Lemon
Tropical hibiscus

Ferns:

Holly fern
Tassel fern
Christmas fern
Autumn fern

A friend (who is an absolute gardening genius and I (who parasitically sucks knowledge out of him) have a blog that is really focused on what works in the Charleston area, check it out if you are interested.

Here is a link that might be useful: My blog

I've seen some of my "must haves" already listed by others!

Since you asked for perennials and not shrubs/trees, here's my recommendations for you to check out:

Arkansas bluestar (Amsonia hubrichtii)
Jerusalem sage (Phlomis australis?)
any bearded or Louisiana iris
butterfly ginger (Hedychium coronarium cvs)
candy corn plant (Cuphea micropetala)
almond verbena (Aloysia virgata)
Japanese tall knotweed (Fallopia japonica 'Tricolor')
ANY daffodil
Indian pink (Spigella marilandica)
Spreading woodland phlox (Phlox stolonifera)
Hardy orchid (Bletilla striata)
Santa Barbara Mexican Sage (Salvia leucantha 'Santa Barbara')
Red hot pokers (Kniphofia cvs)
red verbena (Verbena peruviana)
Pink Surprise lily (Lycoris squamigera)
Red Surprise lily (lycoris sanguinea)
Strawberry begonia (Saxifraga stolonifera)
wild indigo (Baptisia 'Purple Smoke' and 'Carolina Moonlight'!)
ANY aster (like 'Purple Dome')
ANY lily (tiger, LA hybrid, asiatic or Easter)

I see hydrangeas mentioned but I don't see oakleaf hydrangeas listed. They are native southern plants and very rewarding in your landscape.

Having come from Ohio 15 years ago I wish I would have had this forum for advice. I few years ago I recycled a stack of black plastic pots about ten feet tall. Few of those plants survive today. What I have found most important in the south is soil. I live near Lake Murray where the soil is hard rocky clay (hard pan). This will support some native plants but most of my success has been with building retaining walls on slopes and back filling with sandy soils. Don't ask for top soil it will be filled with nut grass that is near imposible to get rid of. I would suggest contacting someone from your local extension service (Clemson in the Columbia area)and have your soil tested, they will tell you what plants will do well. Then select from the list others have posted.