My thought is that you can only raise as many breeds as you have the infrastructure to maintain properly. For most that's one or, perhaps, two. However, a pen of a hens with a cock is not housing breeders. One needs multiple space for cocks and females. Then there are growing-out facilities, which although they can be simple, must be adequate.
I'm not really into discussing "breeds". A breed is what the SOP says it is, I think it is much for valuable to discuss strain because that's what birds are. They are strains. Names are labels. Types are breeds, Strains are what is in you backyard.
If I were to have to choose between a bird that wasn't a top producer but matched the SOP or a bird that was a great producer but did not match the SOP, I'd go with the bird that matched the SOP. As BGMatt pointed out, it is easier to get production into a bird that matches the SOP than it is to get SOP onto a random bird.
I think that the right bird for you in the bird that you want to look at, read about, study, breed, hatch, cull, weight, etc... That's the right bird for you. The internet and lots of books for that matter are full of folks saying things about breeds that they have no business saying. This false information brings people to fall for breeds they shouldn't and reject breeds they shouldn't.
What is rare? Almost every single thing in the Standard is rare in SOP form. The rarest chickens are well-bred chickens. I'd relinquish the rare label. I'd choose a breed or choose a color. If you choose a breed, raise the variety or, if the case be, one of the two or--in the rarest cases--three varieties in that breed that are actually of quality. They are carrying the breed; they are that breed. Color really is skin deep, and I am a firm believer that we need to concentrate on specific varieties in breeds if want anything to survive in high quality at all. There are some breeds with multiple varieties, it might seem like it's a tragedy if one dies out, but it's really not. Lots of color varieties were just someone's experiment that caught on long enough to get into the SOP; however, every breed has specific colors a specific color that is its anchor. That's the on, or those are the few, that people should back, because those are the varieties that will usher that breed into the future. Whenever I see color projects, I feel sorry for the breed, because it's core is being neglected for some fad. Take Cuckoo Dorking for example, much effort was exerted into getting them into the Standard, but to what avail. The Dorking was a dying breed, and here people were neglecting the breed in order to make a variety. Who cares about Cuckoo Dorkings? The only Cuckoo variety of anything that has any hopes of being impactful is the Dominique. Cuckoo in anything else is never more than a fad. While folks were "working on" the Cuckoo Dorking the Dorking itself was slipping away.
Just because a color exists in the SOP doesn't mean it is, or even ever was, any good. There are Blacks and White in many varieties--they are lovely. People often micro-focus their vision on an aspect of a pattern, but the beauty of a flock is in the symmetry and the balance of the type of the birds of the flock. If you're new to chickens, read that sentence again until it makes sense. When you look out at good birds and they make you go, "Wow" it is in their symmetry and balance of type. Color on scrappy birds looks ragamuffin. If it is a specific color that calls you, find the breed or perhaps breeds that own that color and then go there. For example (and this is just my crazy, unfounded, and silly opinion):
If you want Blue and a Wyandotte, you can get Blue Wyandottes. Then you can kick and scream for 30 years until you've got them good and strong (maybe if you're lucky), but to what avail? Blue belongs to Andalusians, and Wyandottes are White, SL, and Columbian. I'm of the opinion that those efforts should go in a direction hat will matter. If I wanted Blue Wyandottes, I'd sit quietly and decide what was more important, Blue or Wyandotte. Then I'd make up my mind and do one or the other. I believe that this would lead to efforts that would actually promote and preserve a breed as opposed to simple self-isolate with a fad that won't go anywhere.
So:
1. If you're raising less than 100 a year, have one breed.
2. If you choose a breed--adopt the primary variety, or ONE of the primary varieties (a hint only two breeds I can think of have 4; some have three; most have two; the luckiest have one)
3. If you choose a color--find the breed or, perhaps, breeds that own that color and go with ONE of them (unless you can raise 200 chickens a year and then go with two of the (maybe))
4. Get the bird that best match the SOP you can find, and it their production isn't where you want it to be, hatch a 100 and start selecting.
5. Don't give up, and if you need a distraction, get a bantam.
