Space inside my carry-on is gold. I approach packing like an engineer. Dimensions for a domestic carry-on are usually 22"x14"x9" (international flights are a tad smaller). Always check with all the airlines you will be traveling on before you go. And measure from the bottom of the wheels to the top of the handle. And get a suitcase with the very strongest wheels that go over uneven surfaces easily. You'll be navigating curbs, sidewalks, cobblestones, carpets, and other hazards along the way. A broken wheel is almost impossible to fix when you're traveling. A good suitcase is well worth the investment.
The other packing "must" for me is packing cubes. Even after a day, your suitcase gets disorganized and messy with constant folding and refolding. Cubes keep clothes folded and fresh. Cubes are also valuable to keep your clean clothes separate from soiled ones. Normally, I organize several outfits into one cube. You can overstuff the cube and zip it up to compress its contents for more efficient use of space. Around the cubes, I'll place shoes and other items. My last tip for women is to accessorize. A pair of earrings or a scarf can take you from a day tour to a nice dinner. Stick to a neutral color palette and have fun with easy-to-pack accessories.
En Route Travelware sells packing cubes with two mesh pockets in the lid for accessories. Just $8.99