Yes, certainly, you can be fine with your PC as a non-mage. If you want a single-class mage, you can make Severn one - he's not a strong fighter, anyway, and that'd be more than enough for magic needs. If you want varied magic support, Severn works good as a fighter/mage or bard, and Teri - as a fighter/thief/mage or thief/mage.
As for healing classes, Korin can be a ranger/cleric, and Nella can be virtually any healer - you could dual her to cleric or druid, or choose a multiclass. Teri is a good enough rogue, whatever class you choose for her. And, naturally, Korin, Holvir and Nella are all good fighters. So, you can choose any, and I mean any class for your PC. Enjoy your game!