You will most likely need to redistribute your attributes at a Class Trainer depending on what you want.
As for changing to a different class, it also depends on what you want. If you want to be a warrior that uses summons then I'd say select the Warrior Class, same if you wanted to be a tanky caster. But if you wanted to be a mage that can deal lots of magical damage and can still hit relatively hard with melee then I'd say go with Black Mage Class.
This is due to each class having passives and perks that suit their respective classes; so whilst it might be possible to mix and mash different powers from other classes, it might not be as optimal as just respecing to a different class altogether for the different passives and perks.
Depending on what you want; some build ideas:
Tanky Summoner (Warrior Class; Warrior Powers and Summon powers): Toughness, Presence, Strength / Agility / Cunning.
Tanky Caster (Warrior Class; Warrior powers and Black Mage powers): Toughness, Willpower, Strength / Cunning / Agility.
Strong Mage (Black Mage Class; Black Mage powers and Warrior Powers if desired): Strength, Willpower, Cunning / Agility / Presence.
I'm pretty sure if you have a look at the Attributes section in-game or
on the wiki, you'll be able to come up with a variety of different builds to suit what you want.
See the below attachment if you want a levelled (and relatively geared with the starting shop gear) character to test your desired build "Spellwarrior":