Welcome to the world of robotics!
My first robot was a Boe-Bot (the controller was a Basic Stamp but they now offer a Arduino version) see http://www.parallax.com/product/32335
. You can follow the tutortials that come with the kit to build an obstical avoidance robot and learn some basic electronics and programming along the way.
The kit has some basic electronic compoents to get you started including several sensors to detect obsticles. The best obstical detection sensors for you are probably Sharp IR sensors; however, these are not included in the Boe-Bot kit. I would recommending purchasing a couple of Sharp IR sensors to upgrade your robot, once you have a understanfing of the electronics and programming associated.
Im sure there are some other good robotics kits out there but I had a great experience with this kit and recommend it to someone beginning robotics.