I think adopting any animal in need of a home is a great thing! But if I wanted to adopt a purebred animal I'd go to a breed rescue outfit.
Over the course of 19 years, I adopted 5 cats, 5 gerbils, 3 rabbits, and 1 hamster. I suppose the gerbils and hamster were purebred, and from the appearance of 2 of my rabbits, I could discern at least some evidence of their breed: Hans was at least partly mini-Rex, going by his size and ultra-fine, soft plush fur, while Franz had clear Dutch markings. Another time at the shelter, I saw a Palomino rabbit- a beautiful animal!- but at the time I was not in a position to adopt a rabbit (I think it was when I already had the two rabbits I mentioned above).
Anyway, for me it's all about personality. My cat Harriet and my rabbit Sony nose-butted me when I first opened their cage to meet them. But another time, I was looking specifically for a cat about the same age as the two I had (Harriet and Riley), but who wasn't that outgoing and might have been overlooked by potential adopters for that reason. She wasn't hostile- just very quiet and passive- so I took her home and quarantined her in my bedroom. Initially she hid under the bed, so I left her alone with food, water, and litterbox- but later that night she crept out, came up on the bed, and laid down with her back next to mine. It later turned out that she had an intestinal impaction which needed to be irrigated (enema) over the weekend. That was probably why she had been so quiet.
All my adoptions worked out fantastically for them and me.
Peasant (1963-1972) and Fluffy (1970s?-1982- I think of you as 'Ambrose' now)- Your spirits outshone some humans I have known. Be happy forever.