It doesn't have to cost a lot to get started. I just had a Dewalt and Ryobi beginner power tool kit to get started (they're almost identical—both were gifts).

Unless you go the hand-tool-only route, the necessities are a good speed square, a drill, a good set of drill bits and a circular saw. Together, those three things (cordless Ryobi are great for beginners and not super costly) shouldn't cost more than $150? From there, spend as you like to make projects a bit easier. My shop has gotten a lot bigger over the last year or so... I've spent quite a bit.

My first real project was a series of planter boxes made of cedar 1x3 boards and cedar fence posts. Considering the cost of the fence posts (cheap), it was a great project to not have to worry too much about material waste.