My favorite old-school-nostalgia character is Mewtwo. I thought he had a really compelling backstory, and I really liked that his role as the antagonist of Mewtwo Strikes Back was more nuanced than Team Rocket's "muwahaha we're evil solely for plot reasons"--he was a psychologically tormented figure trying to find a solution to the problem of his own existence. I also really liked that his character arc in the movie was resolved in a way that helped him as well. I loved that they brought him back as a protagonist a few times after that. I honestly think he was one of the better-developed characters in the early anime and he deserved more screen time.
My favorite current character is Dot from Horizons, because it's wonderful to see a main protagonist who's a technically-inclined girl, kinda blunt and taciturn, dislikes the spotlight and gets burned out by social situations, and basically isn't the usual "peppy preteen who likes frilly dresses" stereotype that was used for May, Dawn, and Serena. Dot reminds me so much of myself. I like Liko for a lot of the same reasons, and I think both girls do a great service to female viewers who are quieter and more introverted, giving them someone they can connect with. I'm also rooting for Amethio, because if you couldn't tell already, I love when antagonists get redemption arcs.