People will rightly say 'Bloodrager' from the ACG... but there's also the very nasty Barbarian Dragon Disciple.
A single Barbarian level will give you Rage (and the ability to take Extra Rage), Dragon Disciple will give you +4 more strength, and of course Sorcerer is Sorcerer. Sorcerer/Dragon Disciple also gives a nice bonus to AC, which can combine with Mage Armor and Shield (and Mirror Image...). You can use more Barbarian to get Rage Powers if so inclined.
Gold Dragon Sorcerer is also very good at casting Scorching Ray, so you've got a dangerous spell to put into a spellstoring greatsword or just to zap things with.
It's not a full-on Barbarian or Sorcerer, but it's got lots of relevant spells and a whole lot of strength damage.
You can not stack Barbarian with Skald. Hybrid classes can not take the base classes that they are composed of.
You can not stack Barbarian with Skald. Hybrid classes can not take the base classes that they are composed of.
You can now; it's explicitly stated in the preamble to Hybrid Classes. Though I don't think anyone was suggesting doing so, unless a post was deleted.
Spell Warrior is an Archetype of Skald. Skald's parent classes are Bard and Barbarian.
However, it seems you are correct. This is a change from the play test that I disagree with. It causes balance issues.
Either way, you can't stack rage and raging song. They both give morale bonuses. I'm not certain what one would gain by taking levels in both classes. IMO, either continue in Skald or go the route that BadBird suggested with Bloodrager and Dragon Deisciple.
Oh right, forgot about the archetype... I thought he was just talking conceptually.
For a significant 'spellcasting warrior' kind of feel rather than just a Barbarian with assorted magic bits and buffs, I would definitely base Dragon Disciple off of Sorcerer rather than Bloodrager casting (though you could (should?) still use a single level of Bloodrager instead of Barbarian). It's not that the Bloodrager is at all bad - it does have some advantages. It's just that there's really no comparison in casting ability, particularly within the level limitations of PFS. Routine access to (uber)Scorching Ray, Mirror Image, Haste, Heroism, etc. vs a couple spells per day and not seeing your first level 3 spell till the very end.
The spell warrior trades out the rage song for a magic weapon song. It still gains rage powers but no way to use them. So the Barbarian dip it to gain a rage to use the skalds rage powers with.
So a 1 or 2 lv dip is what I'd suggests. I'd also suggest doing it your first level. The +4 hp and starting with rage will make the encounters go smoothly. And then you can go skald from there. Get a 2nd barbarian level if you want another rage power.
Edit - as a note, taking 1 lv of barbarian would increase your personal rage song bonus for 7 levels. You'd be able to use your +4 from your barb rage from your song.
Ugh. I am strongly opposed to mixing Parent Classes with a Hybrid Class so I am just going to bow out of the conversation as I doubt I have anything constructive to add. (aside from the fact that I think it would be constructive to disallow the classes from mixing as it was in the play test in the first place)