My very first video game was Sonic Adventure 2 for the Sega Dreamcast. Wow I loved that game. Too bad the disc got corrupted or some kind of crap. All I know is that it keeps giving me errors now.
But, I also have Sonic Adventure 2 Battle (the one you mentioned lol) for the Gamecube. Dude. Amazing game. ALMOST the same as the Dreamcast one but there are differences.
And if you're a Chao breeder, make sure you get a Chaos Chao. I have the Angel Chaos Chao myself, and I bred it so that it has an S-rank in Running. B in Stamina/Swimming, D for Flying/Power. See this site for every detail about raising them.
And about the normal gameplay, I actually got stuck a few times on some of the more difficult hunting ones and had to get help from my friend lol. Surprisingly I still managed to beat Cannon's Core by myself.
Favorite stage: White Jungle
Most played stage: City Escape (ring farming ftw)
Hardest stage: Mad Space
Favorite multiplayer stage: Meteor Herd
Best music: Cannon's Core part 3
Worst music: Kart racing
Best Sonic game since: Sonic the Hedgehog (2006 title, with Silver and Blaze)
2nd place for ^: Sonic and the Black Knight
Oh the memories... you got me going here lol.