I'll likely buy hatchery birds, and this sounds like the best way to go! I know all birds are individuals, but getting several of each breed of interest would give me a lot of chicken dinners and a good idea of what I'm really looking for. And it would satisfy my desire to have a yard full of different chickens just once at least.
I have found that even the "same" breed can be different if you buy them from a different source, so once you find the right one you should buy more from the same hatchery.
As for liking a variety of chickens--there are a few colors that can be interbred with good results. The most obvious are the blue colors (solid blue, or blue-laced-something.) You can have black, blue, and splash birds in the pens, but they are all the same breed. Or black laced red, blue laced red, splash laced red.
If the only one they have to please is you, then you could choose to work with something like Easter Eggers (any color of feathers, no defined physical standard--but you could breed to a specific physical standard that fits your own goals, and let them stay multi-colored.)
Or Turkens (naked necks). A specific standard exists, but hatchery birds often have a variety of feather colors while being semi-consistent on other traits.
Swedish Flower Hens and Icelandic chickens are two kinds that are known for coming in a variety of colors. Unfortunately, I don't think they would be good for your purposes, because they tend to be small, which isn't so convenient for meat.
Or you could pick one breed, and then buy an occasional pullet here and there that lays eggs of a different color to have some variety in your flock. With different colored eggs, you could easily tell which eggs to hatch and which to just eat. White egg layers are often small but lay well, and some are quite pretty, so they would be an obvious choice for eye-candy.
Um, I didn't mean this to get quite so long, but once I start thinking of ideas it's hard to stop