What helped me get going was finding local competitions I could build for. My first foray into robotics was a mini-sumo kit: a Mark III. The kit was complete (I could build a working robot from the bits that came in the kit) it left room for improvement in the hardware (that's my passion, so it was a good thing), it came with no source code (I had to write my own), and it offered me a way to compare my work against something someone else built without risking any damage or loss (mini-sumo robots are not allowed to damage each other.)
I'm not pushing mini-sumo, mind you. I'm just tossing that out as an example. Practically every robot problem I've looked at, ESPECIALLY the simple ones, wind up being much more complicated than I'd thought by the time I'm done. Even building a simple (simple! hah!) line follower can lead you into all sorts of fun tangent ideas like velocity loops, servo tuning, filtering sensor noise, etc.
What I like about building a kit for a competition is that you're guaranteed to build something that'll work, you get to tweak on the hardware, the electronics, and the software, and you get immediate feedback on whether your changes had any effect on the outcome.
Past that the sky's the limit. As far as my Mark III goes, I'm gutting it so I can replace the processor with an Orangutan, I'm eventually planning to swap out all the sensors for a Theremin Vision II system, and I hope to have it running in a competition in late November this year. Should be fun!
P.S. Shame it's not a biped, but my Mark III ran right around $100 US, and my line follower ran only slightly more. They're in your price range!