I would guess a dual Normal/Flying would be ok against Fighting types (If that counts), since the dual Flying cancels out the weakness against Fighting. Or, Girafarig is part-Psychic which also neutralises the Fighting-type weakness. Just a shame Flying types and Girafarig aren't all that strong.
Personally I don't think you can go wrong with Snorlax, the strongest normal-type in the RBY games, maybe even in GSC (His base stats are 540, which is joint-third strongest if you don't count legendaries). He also has the ability to heal himself, has high HP, is a massive pain in the ass with leftovers and can learn a varied moveset.
Hope that helps ^_^