I just started with electronics a few months ago, too. The things I have found useful: LED's, resistors, voltage regulators, MOSFET's, BJT's, RGB LED's(fun), and also a speaker/piezo disk(also fun). Motors are also cool, but make sure you have transistors and diodes. Capacitors are always good to have, and so are 555's( I got like 100 on eBay for about $11.) A cheap LCD(eBay) and various other displays(LED matrix, 7-segment, bar graph) are useful. Switches are very useful if you don't want to unplug/replug things in for power.
I'm not sure what kind of hook-up wire you have, but having both the straight and flexible kinds is useful. Before I had the straight ones I had jumper bundles so thick I couldn't see any of the components.
As far as tools go, a multimeter, screwdriver set, helping hands, a knife, and wire cutters are helpful.
Also, if by "local electronics shop" you mean Radio Shack, NO. $1.69 for a red LED?! No thank you. eBay=cheap, cheap, cheap(If you can stand the wait).