My personal favourite world is Tirane. Yes, know it is labelled as "core" but I found its description in the Colonial Atlas very interesting. Not least because of the developments in 2320 AD that takes some of the nations on Tirane as steller nations with colonies of their own. That gives the setting an interesting twist.
Core: Tirane, for the reasons given by Waldemar.
French Arm: Joi. Joi is a politically diverse world--with five colonies, Joi hosts most major human settlements than any world but Tirane. Elysia's independence further complicates matters by introducing radical anti-colonial ideology into the mix. Finally, the ecological themes of Joi, with a complex but fragile biosphere vulnerable to its Terran counterparts, anticipates the themes of games like
Blue Planet. Beowulf and Nibelungen would be close seconds, because they're unearthly garden worlds and because they host some of the largest and oldest colonies in human space.
Chinese Arm: I've a soft spot for Heidelsheimat, I'm curious about Chengdu, and Home of the Mother could be quite interesting, but I'd have to say that Kanata appeals to me. No, it isn't because I'm Canadian.
It's because Kanata is an appealing example of a non-Earthly garden world that offers alien ruins besides. (C'mon, you trust Canadians with psychic weaponries produced by ancient alien races, don't you?)
American Arm: I'd have to say either Kingsland or Botany Bay. Both of the Australian colony worlds have interesting histories and biospheres, and with the opening up of the Ylii front they have the potential to really boom.
Kafer Space: I don't have my
Kafer Sourcebook with me right now, but I'd pick Lambda Serpentis IV and V. The local suzerain, Gvah, ruled over a planetary system that had one garden and one glacier world, with a population that was reputedly relatively peaceful by Kafer standards. Wouldn't it be interesting to see what was there now?