The first thing will need a 5 volt power supply. Lots of integrated circuits and microcontrollers need 5v (getting close like using 4.5 volts is also acceptable). Some projects may take larger voltages, but 5 would be the starting point. This power supply should be able to handle at least 300mA, finding one capable of more is always better. You will also need a breadboard, so you can just poke wires and components in and the connections will be made automatically, no soldering required. Get wire strippers and needle nose pliers if you don't already have them. One thing that is extremely helpful is a multimeter. It should at the minimum be able to do AC/DC voltages and currents, resistance, and continuity tests.
You will also need an assortment of:
wire - 20 AWG or thinner (I generally stick with 22)
resistors - 1/4 watt, values from 100 ohms to 1 megohm
capacitors - various values of electrolytic (microfarads range) and ceramic disc / monolithic (pico- and nanofarad range)
transistors - general purpose bipolar junction NPN and PNP
diodes
LEDs
That'll get your cabinet of components started. You might also want to pick up a 555 timer, an operational amplifier, some logic gates like a NAND gate: 74LS00, Inverter: 74LS04, AND gate: 74LS08, OR gate: 74LS32.
If you've found any simple beginner projects that you'd like to try, they will have a parts list, so be sure to get those too.
And when things just don't work out after hours and hours of effort, perhaps the most important tool is a hammer. :twisted: