Instruction should precede gear purchase..."Climbing" is a pretty broad term - rock, alpine, hiking to high places are all "climbing" and need different kinds of equipment.

A good general guide is "Mountaineering; Freedom of the Hills", 50th Anniversary Edition..  It is a good guide, but learn the basics from a good class or a knowledgeable mentor.

It is safe to say you will need appropriate foot gear and clothing, and at least a minimal first .aid kit,along with a water container and some sort of pack.  For technical stuff, you will acquire a harness and helmet, along with all sorts of goodies (rope, carabiners, protection pieces, etc.) but those can wait.  Get instructed first. 

There is a lot of good information on this website, as well.