Side note: any class can kill a spider swarm in core with a sufficient quantity of alchemicals. This is obviously an expensive solution...

A core-only Cleric with the Magic and Travel domains is pretty good. Magic and carefully spending wealth on partially charged wizard wands/staffs means you effectively have access to most core-only spells. The Travel domain grants some nice spells and gives a Freedom of Movement at starting at level 1. I haven't done a detailed comparison with Wizard or Druid but maybe that's worthwhile?