Hi - does anyone know of a first Level spell providing a Climb speed?
Nope looks like your best bet is spider climb as an lvl 2 spell.
If you only need a one off use you could get a potion of spider climb for around 300-400 gold I think but don't quote me on the price.
Catfolk and goblins both have alternate racial traits which grant a climb speed (which you'd have all the time, not just for the duration of the spell). Of course, that's little help if you need to be a different race for some reason, but it is a good way to have a climb speed at level 1.