I hated the newborn stage. They do nothing very interesting and demand, demand, demand. I have this theory that parents who liked the newborn stage have either selectively forgotton how utterly draining it is or prefer to have complete control over their kids.
DD is MUCH more fun now she's a toddler, I love all the fun things we can do together and I love watching her explore the world. Sure the tantrums are a pain, but I'll take tantrums over 2 hours sleep a night any day!
Not really qualified to answer the next two stages, but I'm interested in other people's opinions.