An important note about starting level:
- Arcane Trickster with Wizard starts at level 7.
- Arcane Trickster with Sorcerer starts at level 8.
Also note that you only get Sorcerer abilities up to level 4. After that you will be gaining levels in Arcane Trickster, so you will only get the Bloodline abilities for level 1 & 3. You will only get the bonus spell from at level 3, the bonus spells for 5+ won't apply.
With that in mind, here are some bloodlines that make sense based on their bloodline powers. You're only going to get the first bonus spell, so it's generally a smaller consideration.
From a combat perspective, the Arcane Trickster is normally about throwing Ranged Touch spells and dealing Sneak Attack damage. This trick does work and can do real damage. A single Scorching Ray deals 4d6 with no save and a very low miss chance. If you are stealthy / invisible, it deals 4d6 + Sneak Attack. If you manage to roll a critical hit (natural 20 + confirm), it deals 8d6 + Sneak Attack.
The following provide a Ranged Touch Attack in the form of a Ray that combines with Sneak Attack. All of these also get some form of elemental resistance at 3rd.
- Aberrant (1d6 base acid)
- Celestial (1d4 base vs evil)
- Djinni (1d6 base electricity)
- Efreeti (1d6 base fire)
- Elemental (1d6 base of your type)
- Marid (1d6 base cold)
- Shaitan (1d6 base acid)
That stated, these Ranged Touch abilities may or may not be useful for a long period. Generally by level 5 you are packing a wand of Scorching Ray and that just becomes your tool of choice. It costs 4500gp, but that 50 charges + your existing spells can go a long way.
Note that if you want your character to melee and flank, you may want to look at some of the Bloodlines that enhance your weapon. The following provide your Weapon of Choice, generally extra damage on your physical attacks.
- Boreal (frost)
- Stormborn (shock)
- Djinni (shocking grasp bonus spell)
- Martyred (lots of melee worthy abilities)
Protean lets you generate Tanglefoot Bags, which may be useful if want to go the flanking route.
So I don't think you can go wrong with the Elemental Bloodline. It's really flexible and combat-friendly. The ability to change the elemental types of your damage spells is actually a big deal. Most damage spells are
[fire] but many common creatures have fire resistance. Being able to pick
[acid] instead means that you have a backup way to bypass that resistance.
I only have the core rulebook and advanced player's guide.
You don't really need all of the books, just take a look here. They are broken out by "official" and "unofficial" versions.
Also definitely take a look at the Ninja class for your "rogue" levels. Ninjas are similar to Rogues, but they get a ki pool that powers some "ninja tricks". The Ki Pool is based on Charisma, so you'll get large pool. You'll likely only get one trick (level 2) but take a look at Shadow Clone (basically mirror image) or Vanishing Trick (invisibility as a swift action!). Being able to go invisible as a swift action means that you can generate a sneak attack in a pinch.