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I'm playing a rogue 3/ sorcerer 1 as a prelude to an arcane trickster. Since I expect to be spending more time in melee than most spellcasters, I want to have pretty good AC, but the armor I have now (studded leather) has a 15% arcane spell failure chance. I checked out this question, but most of it only applies to 3.5, and I'm playing pathfinder.
How should I deal with arcane spell failure from armor in Pathfinder?
It'll cost you two feats, but since you're a Rogue, it should only cost you the one.
Every turn, spend your Swift Action to reduce the spell failure by 10%. This would be great if it didn't require you be CL 3, which you will eventually be, but not realistically soon.
Mithral Armor reduces spell failure by 10%, but it doesn't transfer to newer suits when you want to upgrade. Be prepared to wear the same mithral shirt every day for the rest of your campaign.
One thing very few people think of is just avoiding spells that require movement. If you work strictly with verbal spells, there's nothing you need to worry about.
Still Spell, costs a feat and a spell-level, but makes all of your spells Verbal only. As a Sorc 1, you're never going to be able to benefit from the feat itself, though. Alternatively, you can get a Lesser Rod of Still Spell for your Level 1 spells. Keep it at your waist or in a wrist sheathe for easy access and out the window go your chances of failure.
The other option than the one Axoren suggested is to not worry about wearing armor at all. The first level Sorcerer / Wizard Spell Mage Armor provides a +4 Bonus to Armor class that even works against Incorporeal creatures, Making it better than any light armor that you could get at that level without providing any of the drawbacks such as armor check penalty (Which rogues don't like because it affects a lot of their skills) or Arcane spell failure.
A Wand of mage armor would cost 750gp for a first level caster and a first level spell, which lasts for 50 encounters, or one hour per casting. Later on you can get higher level castings of the spell to make it harder to dispel if you're the target of such an effect.
As early on in the game as you are I would not worry about armor until you start hitting the levels which you get moderately enchanted items, since you'll have to take the Arcane Armor Training feat to remove the failure chance. Once you start getting armor with useful enchants and high level enchantment bonuses you can move on from mage armor while establishing a base of power with other useful items. (Such as a Ring of Blinking)
The only downside to the Mage Armor method is if facing arcane spell casters above fifth level they have access to the spell dispel magic, however there are better uses of their action economy than dispelling a 1st level spell off a rogue, provided you're remaining stealthy and undetected they shouldn't have the opportunity to do so. If you want to prevent dispel attempts you can get a heightened wand of mage armor later on to compensate for the higher caster level.
