I would mix the colors in a more random pattern. Since pink is basically red + white, a random mix might create a more appealing blend than if they were arranged by color. The eye will be drawn to the most dominant color in the row, so breaking up the colors will keep the eye moving around.

Ah, see? You sound like you know what you're talking about. I'm very type A, so I'm just no good at random-ness. I will keep this idea in mind for sure.

Yesterday I cut flowers from my garden to take to a relative. At this time of year, the flowers with stems of any length are mostly white, pale pink, medium pink and red (though I also added some yellow-white marguerites).

The colors worked well together. The very dark red columbines were fine with the Former Owner's medium pink roses and the standard pink-red coral bells. On the other hand, the Robinson's Red pyrethrum, which had just bloomed for the first time, turned out to be a horrible magenta. Not only did it look awful with the dark red columbines, but it looked awful with the coral bells and the pink roses (and it's not long for the bed it's living in).

Which is all to say that how I'd plant the peonies would depend on how the individual shades do next to each other. If some of the colors shouldn't be seen together, I'd make a random mix as jenn suggested. But if the colors are more like different shades from white to red, you might consider that sort of planting arrangement. Start with white on the sides, then move through the pinks from lightest to darkest, ending with red in the middle. Or have red on the sides and white in the middle. I'm not guaranteeing such a progression would work well or look good, but depending on which shades of pink I had at my disposal, I'd consider trying it. (However, I'm not a pro, so be warned.)

Well, here's what's funny - I've got 3 different pinks and of course they're not blooming yet. I can't remember exactly what they look like. One is ancient and was here when we bought the place (property is 100+ year old farmstead), one is a hand-me-down from a friend who got it from a friend. Another was purchased at a master gardener perennial sale and was only labeled "pink". I'm confident they'll all mix well with white and red and I'm pretty set on the random idea. I actually made little pieces of paper, one for each plant, and drew them from a hat to determine order of planting. I did it 4 times before I saw a pattern I felt good about.
Here's my next decision to make... I should probably cut any flower buds that develop this year, yes? It's a bit late to be dividing peonies, and stems are already up to 10 inches high. How necessary do you think it will be to prevent flowering this first year? Makes me sad...

Peonies are best divided in the fall. I would leave them be, take pictures of them in bloom so you know the colors (if the new ones bloom this year - they may not...) You can use the pictures to play with arrangements, then divide and replant this fall.

I like MTO's arrangement of shading from light to dark - either the length of the bed or having the dark red in the center and fading out through pinks to white on either side. Last summer we replaced the rose on the swag with clematises (no thorns!). I have them arranged so they start off red at one end, shade through pinks to white, then to pale blue, to deep blue-purple. Having the reds at the 'near' end (at the south gate entrance to the back yard) and the deep blue-purples at the 'far' end should make the alley look longer - in theory at least. Reversing the colors would make it look shorter. However, I find clematis notoriously mislabelled plants. Since I wasn't able to find them all in bloom, I won't know if it works until they get big enough to bloom - and that may not be this year... Playing with color arrangements is fun :-)