Yes it's an undefined bonus - same with the Unearthly Grace special ability Nymphs have, while the Divine CHA to saves is a Luck bonus.
You can look like a dragon by spending trait points i guess, wait on HM for that. I'd definitely go for fighter, you will need a ton of feats to really make an effective God of War. I should know, Heliasillyel is just starved for feats, as i want her to be a Bard/Sorcerer hybrid, i'm just wandering where the hell am i going to get all the archery feats from...
On the other hand,
Divine Weapon Mastery has a prerequisite of Fighter 20 and grants you free Weapon Focus, Weapon Specialization, and Improved Critical feats when wielding any simple or martial weapon.
You should go for
Divine Battle Mastery (which still needs lots of feats to take), and of course, is the pinnacle for any War deity.
To put it in simpler terms, Salient Divine Abilites are far far greater and more important than your Classess. In this case, your class levels and features are prerequisites to your SDAs and that's about it.
For example I'm planning for Heliasillyel to go Divine Bard, Irresistable Performance, Divine Archer and Divnie Metamagic. So i will be Bard 20 first, and then get 20 levels of Sorcerer and get the Epic Feat that allows me to cast two Quickened spells per round.
Which reminds me, Alter Reality does not substitute for caster levels. One can cast heavily amplified 9th level spells with spell slots above 9th level with Divine Spellcasting and of course, with my aforementioned biuld (don't you dare steal it

) a deity can cast two quickened 9th level spells and one regular 9th level spell amped up to say 13th level. And, those can be channeled trough a metamagic rod for example....