Im going to list each of them and their counters, Ill Go by Dreamland and Hyrule for stages because its more stage selection than anything for most of these chars
Pikachu: Matters which stage, on HC probably Fox or maybe Falcon/DK. Dreamland is broken for Pika, if you can ban it ban it, otherwise probably Fox or DK, no character does especially well vs Pika so none of these are sure wins, they are more even
Kirby: Fox, Luigi, DK, Jiggs, Mario on HC Any of those besides Fox on DL, no real big counter but not as hard a matchup as Pikachu
Fox: No real counter on HC if anything Mario, on DL, DK, Mario, Pikachu, Kirby MAYBE
Ness: Most characters do reasonably well vs Ness, I think this is the only matchup besides Jigglypuff that Samus counters, DK does well on both stages, so does falcon, Pikachu, Kirby, Fox, pick more of what you think is your best character
Mario: another good character with no real counter besides on DL, Pikachu/Kirby on DL, maybe fox and probably Pika on HC
Falcon: Mario and Fox on both stages, Kirby does reasonably well on both, Pikachu is basically even on HC, Jiggs does well vs Falcon on HC
Jigglypuff: Samus on HC, DK BY FAR on both (grab into giant punch kills incredibly quckly), Luigi also does really well
Luigi: Fox probably on HC, DK on DL, no real counter but Luigi doesn't do that well either
Yoshi: Kirby, Pikachu, Fox, no others needed (LOL)
Link: DK on DL, Fox on HC, Falcon (?) on DL, Pikachu/Kirby on both
DK: Fox (maybe) on HC, maybe Mario on HC, no big counter on DL, maybe Pikachu on both MAYBE, Luigi does pretty well also, Samus does well but only on HC, Link on HC also maybe
Samus: Pikachu, Fox, Falcon, Samus doesn't do that well either vs anyone but Ness and Jiggs
There really aren't that many huge counters in smash 64, that is one of the main reasons why my favorite smash is smash 64