I think I better start a little higher on the nomenclature than species.
Family: Cactaceae (Sure, agave and aloes are nice, but give me a cactus. A real cactus, none of that euphorbia nonsense …)
Genus: 1. Opuntia, 2. Mammillaria, 3. Pachycereus
Species: Anything from 1 or 2 above makes me incredibly happy.
My collection: I think this is what you were asking me (probably), so here are my favorites:
Opuntia ellisiana (Tiger Tongue Prickly Pear)
Pachycereus marginatus (Mexican Fencepost)
Mammillaria bocasana(Snowball or powder puff cactus)
Opuntia imbricata v. viridiflorusI(Santa Fe cholla)
Neocardenasia herzogiana (Caripari)