Do you know how much sun? If it goes from first thing in the morning through 1 or 2 PM you can grow full sun plants, but if it's only for two or three hours, that changes your choices. I have a red/pink/white bed, and one thing I've found is that I needed to choose between orange-reds and blue-reds since most plants seem to tip slightly one way or the other and IME they didn't mix well. I ended up choosing the bluer tones, so the first suggestions will be in that zone.

Clematises 'Rebecca' (red) and 'John Huxtable' (white).

White allysum and cosmos are annuals that will reseed IME.

A lot of the Oriental lilies fall into the bluish-red category or white.

Dianthus has some varieties with just white such as Greystone, a spring bloomer; Brilliancy, a bright rosy red, bloomed for me all summer before the voles ate it last winter; and there are many that are mixed red and white.

There are a whole range of Dahlias in various reds, both pink-reds and orange-reds. Some even have maroon leaves.

Depending on the type, peonies can be either bluish-red or orangish-red. Just look for ones that say they have strong stems or plan to grow them in support hoops.

In the more orange-toned reds, look at the various Asiatic lilies, Canna and Croscosmia (though they may need more sun than you have), and Lobelia cardinalis (cardinal flower).

I love white petunias, but I have no idea if you can direct sow them in your area....

Deep red 'Blazing Sunset' geum is a favorite in my red bed.

How about some roses!

Zinnias come in multiple heights, multiple flower forms, and multiple colors, including red and white and mixed red and white together. They could be used prominently early on while perennials get established and then as fillers later on. They are easy to start from seed.

Martha

Whorled Milkweed is about 18" high with clusters of tiny white blooms about 4" across. Plant those in a group for late summer blooms. I also like the fall-flowering white onions/allium and they come back. I planted Red Riding Hood Penstemon and what a show it put on this spring.

Heidi

Midnight Marvel hibiscus has huge deep red blooms with dark foliage.

An old fashioned and truly red perennial is the Lychnis calcedonica, called the Maltese Cross. Because pink, orchid, purple, etc, are not my choice, I grow any number of white clones, like the white Phlox 'David', 'Miss Lingard' and Phlox sublata and stolonifera. Also Mazus repens 'Alba', Irises tectorum and reticulata 'Alba, the white Obedient Plant, Physiostegia virginica, and more. I have not been successful with the Cardinal Flower, but you might be.

docmom, my mother planted a mixed border of red zinnias and white zinnias this year from seed and they turned out beautiful. She really wasn't crazy about how high they got but because the plants and blooms are so nice she's getting all kinds of compliments.

Cardinal flower is a true red and a hummingbird attractant. Mine self seed a little so have had these for years and love them. I found lychnis cacedonica too reddish orange and gave it away. And yes, I tried several sources with the same result.