In the original for N64 I used either Fox or Captain Falco. In the gamecube version I used Doctor Mario, or Falco.(I used to own in GC with Samus, but I stopped playing.) But the best character is unfortunately Kirby. He has the most powerful skillset if someone knows how to use him, which is really hard. Hence everyone thinks he sucks.
Who's Tink? Toon Link? If so, then I agree, he's awesome. Can easily keep up with Fox's speed (in moves anyway, not running), and is extremely versatile, like you said.
Another awesome character is Snake. Incredibly annoying if you're fighting him in 4P free-for-all, due to the excessive use of mines/grenades. He has enough quick moves to round him out. Like a one man army.
1. Kirby 2. Meta Knight 3. King Dedede I like the Kirby characters because they can jump multiple times, but I especially like Kirby since his hammer's always good for launching enemies. My least favorite character would be Olimar, he just... Sucks.