Ice Climbers aren't very good when newbies play them. I mean, yeah newbies aren't very good, that's the point of the term, but as soon as you can seperate Nana and Popo newbies will become even worse, so I wouldn't recommend banning them.
As for the best character to punish newbie mistakes: Ike. He's easy to play, packs a big punch, moderately fast, one mistake can easily cost your opponent a stock. If you can chain grab then Dedede is a pretty good choice too, especially since he can always keep the opponent at bay with his Side B. Snake is also good at surprising people that are too careless with the mines and C4 stuff. Donkey Kong also isn't a poor choice.
In general, the hard hitters are just great at punishing mistakes,I'd say Ike is the best though.