Kobolds suffer a -4 penalty to Str and a -2 to Con in exchange for a +2 to Dex. They sort of make up for this by being naturally tanky: +1 Natural Armor and +1 Size bonus to AC. Despite being hard to hit however, kobolds are 5% more likely to succumb to any Fort save they've gotta deal with than most other adventurers and have 1 less HP/HD than other PCs.
In short: this race would likely avoid melee or situations where they might be threatened by poison, toxic gasses, heat exhaustion or other attacks on their delicate constitutions at any cost. If they DO want to engage in a life of adventure they'd then gravitate towards classes that mitigate or negate these penalties, while exemplifying their strengths.
They have a base move of 30' with decent Dex and the Size bonus of +1 to hit with attacks. This race from level one on would be terrific at hitting with Ranged Touch attacks. They'd also focus on weapon-based classes that either have magic and bonuses baked in or grant a lot of feats or finesse to their attacks.
Any weapon damage will be at a disadvantage for kobolds. Even if they get Dex to damage, they start from the Small size for damage dice. Kobolds might go into a class or choose a racial build that gives them lots of natural attacks, figuring that overwhelming amounts of attacks per full attack round might assuage this challenge, but more attacks means less accuracy per attack. Unless lots of natural attacks are coupled with a Full BAB class, this just isn't worth it for most kobolds.
They are natural buffer/de-buffers. High Dex and tanky AC, coupled with a 30' move means that if they can finesse a Reach weapon they can be mobile around a 30' battle area, deliver Aid Another bonuses, use skills and feats based around Dex to move through threatened areas with no AoO's, be hit slightly less than most adventurers by those few AoO's that DO trigger, can use their alternate racial trait Shoulder to Shoulder to great advantage if they're with other kobolds, and then if the kobold takes a class that grants spells or abilities that buff the party their tankiness will help them stay alive round to round to USE those abilities.
However there's also the alternate racial traits Frightener and Wyrmcrowned. If you de-buff using Fear or the Intimidate skill, you're now casting spells with the Fear descriptor at +1 DC, Intimidate is always a Class skill and ON TOP of that, you get a +2 Racial bonus on the skill. Sure, youre slightly less good at Stealth now and you lose your Natural Armor, but by level 3 you're casting Fear spells with potentially a DC 18 or better save, or you're using Intimidate with a minimum of +10 or more.
So... this race would gravitate away from melee weapon damage builds unless it couldn't be avoided. Classes that grant bonuses to Fort saves, abilities to resist or avoid poisons, toxic clouds, and such, and just generally focus on being effective from range would be a natural synergy. Kobolds can be excellent support PCs in large groups.
Look for any spellcaster that plays into that buffer/de-buffer role. I'd also throw Summoner out there for their ability to function well in groups. I imagine that Monks or Brawlers would appeal to melee-hungry kobolds, with perhaps more zealous ones looking to Warpriest. I mention these b/c a portion of their attacks will always increase in both damage dice as well as bonus damage as a function of the class.
U-Rogue leaps out at me. Kobolds are great at Stealth and "skill monkey" roles. Add in that you've got baked in Dex to damage and SA damage, Evasion to avoid AoE threats that might target Fort, and finesse as a class function and you've got lots of synergy for a kobold.
Honestly, outside of draconic sorcerers kobolds get no really great shakes as arcane spellcasters. They've got no bonuses to mental stats and their already low Fort save becomes even more of a lead weight if they're playing a Wizard or Witch where Fort is their worst save.
Draconic blooded sorcerers however can dump their NA bonus for Draconic Affinity and cast spells as if their Cha were 2 higher. If you didn't multiclass and just intended to go Sorcerer for 20 levels, with a 20 point buy you could just spearhead most of your points in to an 18 Cha, take Draconic Affinity, and be dropping level 1 spells with Spell Focus from one school at a DC 17 save.
I focus back on Divine spellcasters though only b/c many Divine casters have a good mix of defensive and buff/de-buff spells and gear. This synergizes with the kobolds' natural tankiness and other de-buffing options I've mentioned above. I feel like a lot of them would go Warpriest; if you want to go natural weapon your bite will only increase in damage dice over time, you've got a couple bonus feats to shore up said natural weapon attacks, decent Fort save, plus spells, Fervor and Blessings to make sure you and your allies are buffed up. You could ALSO build a Cleric built around Necromancy and using Fear effects.
