Basic Electrical Components

There are quite a few tutorials here, to help you get started with arduino. They are basic programs to learn the use and most of the capabilities of the board. I scanned quickly through, to make a list of the basic stuff you will need, so here it goes:

LEDs:

Most programs require up to 3 LEDs, so buying 2-3 of each basic colors (Red, Green, Blue) is a good idea, so it isn't very monotonous. They are quite cheap, they will not be a great expense.

Resistors:

• 100 Ohm
• 220 Ohm
• 4.7 KOhm
• 10 KOhm

I think those are most of the resistors used. Buy 2-3 of each, they are quite cheap too.
Buy more of the 220 Ohm ones as they are used with LEDs so you many need more at the same time.

Potentiometer:

These are varrying resistors, you change it's resistance using a screw on top of it. The one used in the tutorials is a 10 KOhm.

Breadboard:

This is a MUST have for anyone who likes electronics. It's a board that helps you build and test circuits very fast without having to solder. Read here if you don't know what it is.

Switches, Wires:

Wires are needed to build circuits so i don't have to go more into this. Switches are used for input, button switches, which is the most common type, i think will do just fine.

Miscellanious stuff:

8 Ohm small speaker, a speaker used to hear the sound generated by the board, in one tutorial.

Photocell and Force Sensing Resistors. These are sensors, the first is used to detect light, the second to detect force.

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Those are the basic components needed for building the circuits used in the tutorials. There are also more advanced sensors in advanced tutorials, like 1or 2 axis accelerometes but it think this list is enough for anyone starting out.

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Happy Tinkering!