Welcome to LMR btw. As far as parts go, some of the components (like small gear motors. microcontrollers, sensors) are hard to come by in brick and mortar shops for the most part.
I recommend a look at the Start Here Robot that Frits made. His design is very minimalist yet charming and is a good look at what you’ll need. Some use an ultrasonic sensor instead of the infrared rangefinder used. Some use an Arduino instead of a PICAXE. The essence is the pretty much the same though.
I really suggest a kit for your bot I started with the Boe-Bot from Parallax. It’s a really great kit that comes with everything you need to keep you busy for a long time and a HUGE text book that is amazing. It teaches you lots of the basic concepts, Parallax is known for their exceptional documentation. Even if you go with an other kit can download the text from their site it is really good. LMR member Chris the Carpenter’s company Rocket Brand Studios also has some new kits that look really cool and are available using either Picaxe or Arduino. So be sure to check them out too! Kits are great because you know all the parts will work together and you have instructions based on the exact parts you have. It takes a lot of pressure off and almost guaranties you will actually get something blinking and rolling around. =) You can see some video of my Boe-Bot here.