A mithral buckler (1,015 gp) has 0% ASF and grants +1 AC. It also has 0 Armor Check Penalty, so you take no penalties for using it if you’re non-proficient.
A mithral chain shirt (1,100 gp) has 10% ASF, and grants +4 AC. It also has the 0 ACP thing. Unfortunately, a 10% chance of failure in an emergency is a very bad idea, and I can’t find any great way of reducing it further. Pathfinder does have some feats for this, but they are unbelievably awful. Don’t take those.
There’s also, apparently, a few different Celestial armors, like this Celestial Chain Mail, which if you back-calculate its costs and bonuses and things, reduces Arcane Spell Failure by 15% for 1,200 gp. If you can then apply this to Studded Leather or Parade Armor, you get 0% ASF and 3 AC.
Celestial armor, mithral, bucklers, studded leather, and chain shirts are all part of Pathfinder core as well as on the PFSRD. Parade armor is from Adventurer’s Armory, apparently, but also appears in the PFSRD in the Armor Section.