You wan a Dragonborn supremacist! Cool!
You get to belch fire as a sub-racial feature.
Eldritch Knight has the Burning Hands spell - a fantastic "firethrower" spell. Good for clearing out rooms with lower level enemies.
The Good People here make a compelling argument with taking Sorcerer - as your "casting" side - to make use of your high CHA from being a scary, ugly alien.
I like the Fighter/Sorcerer path you imagine.
Strong, hawt! and dumb - (as usual in DnD) is the way to go.
STR, CHA, CON - the rest don't matter that much.
BTW - a Light Domain Cleric has "burny" spells - you could roleplay those as not being "radiant" but "firey". But here you'd need WIS of 12-14.
