Don't screw around with BFP, it's gone seriously downhill. Yes, RC3.8 (not 4, I don't think 4 exists unless they renamed 3.8) is fun, but EBFP is where it's at now. You can find that (if you go through the mess that is their website) at
www.ebfp.tk . At least I think that's the right link... anyway, it's like RC 3.8, but with about 50 more characters, better sounds, and better animations. The problem? No servers. And I mean no servers. You just can't find any at all, not with the all seeing eye or in game, they don't exist. Only download it if you are going to contact someone who is willing to join before you host it.
Urban Terror is also a decent Quake 3 mod. It has a huge following, though personally I think it's gone downhill since 2.4 . Whatever; it's still a good modification at heart. (
www.urbanterror.net)
A better alternative if you enjoy Counter Strike (without the cheats) would be Navy Seals Quake 3 (
www.ns-co.net). Highly addictive gameplay, smoother animations and better models than CS. Experience point system instead of a buy system. Beta 1.9 is just around the corner (it's like ESF beta 1.1, everyone is convinced that it'll be out next week, but it's more likely a month or two away).
Yeah ok, so neither of those are anime based, but they're still worth looking into if you haven't. There aren't any really good (or half way decent) anime mods for Quake 3 that I know of. I thought they were going to release some kind of anime battle modification with a bunch of different characters but I guess they scrapped it. Life happens...