If you are talking about looks, I would have to go with the ZGMF-X88S or RGX-03 (it all depends on when you are talking about in the series) from Gundam Seed: Destiny. Also, I really do like the the original Tallgeese and the Tallgeese II from Gundam Wing because of the practical realism of them (Talgeese and Tallgeese II are fairly lightly armed in which it gives them decent power while still having very nice mobility after they are out of ammunition ) (I do not like the Talgeese III for reasons I am going to get to).
My main problem with Gundam in general is that when you get past the 08th MS Team (which is probably one of the best Gundam animes because it is very realistic) or the original Gundam (granted the Mark II isn't bad either), you start getting nothing but uber Gundams. Which there is nothing wrong with amazingly powerful Gundams that dominate anything they face, I just am not really a fan of it that much.
As for characters, I'm definitely a fan of Treize Khushrenada from Gundam Wing because honestly, he is just a good character by being fairly deep. I also really liked Char Aznable from Zeta Gundam (obviously moreso when he became Quattro Bajeena because when he looked really goofy being short and having that helmet on him).
Truth be told, though, I thought that the whole Gundam series was OK at best as an anime. Mainly, the good ones evened out the bad ones to make it OK.
As for the game itself, I really thought that the whole lack of depth in the gameplay was going to make this game really boring, really quickly. However, I rented it (because it really isn't worth the 50 bucks or however much to get it new when it just came out) and have already logged over 10 hours on it and I just can't stop.