I don't think there is an actual difference between a Spellsword and a Battlemage, just two names for the same thing.
A paladin, however, is usually a holy warrior who focuses on melee and restoration/anti-undead magics. Naturally they try to do as many good deeds as possible and usually wear heavy armor.
Dunmers make excellent battlemages, redguards are good paladins. Breton is a good choice too for a battlemage.
Also yeah a nord dragonborn is probably the canon lore for what's going on.