I have an extremely rare breed too. There just are few or no birds to acquire stock from so I have to work with what I have.
Obtain a copy of the SOP if there is one for your breed or try to find standards for the breed so you know what you are trying to achieve.
Then the best you can do is hatch as many chicks as possible. Identify those most representative of the SOP and cull or sell off the rest. Out of every 100 chicks, you may get 5 good birds. Then try to establish 2 or 3 separate lines depending on how much room you have. Multiple housing options is essential.
Ideally try to get some unrelated stock to introduce for genetic vigor. However, if they have flaws, you could be going backwards.
In these separate lines, breed the best male to the best female. Then breed the best pullets of that mating to the sire and best cockerel to his mother. Then best granddaughters to grandfather, best grandson to grandmother and so on for 7 generations and then cross the lines.
I can usually identify almost half of the chicks at hatch that I won't be using for breeding. Then as they grow I narrow it down more as characteristics show themselves.
I have to achieve extremely dark eggs, all black feathers, white earlobes, carnation comb, dark slate legs, 'horn of ox' beak, and then there is the shape of the bird.
I only hatch from the darkest eggs, eliminate chicks with off colors or too much white and legs that are too light. As they mature, roosters that don't have nice white lobes don't stay. The carnation comb for now has been prevalent but they could be better. It takes a really long time to get it right, especially with so many unusual traits needed to achieve.
Then all you need is a predator massacre to set you back years. A few years ago, mink killed $4,000 worth of my birds.
What breed are you working with?