Resistors:
A few of around 220R or 330R range for use as series resistors with LEDs. These limit the current so the LED and the Arduino outputs are not damaged. A few of 10K for use as pull-up or pull-down purposes for switch inputs. These prevent Arduino inputs "floating" and giving random readings (although you can often use the Arduino's internal pull-ups). While shopping, get a few other values like 1K, 4K7.
Capacitors:
You may not need many at first, but if shopping, get some 0.1uF for use as "isolation" and noise suppression circuits and some "electrolytic" ones in the 10uF to 470uF range for use as "local power reservoirs".
Potentiometer:
10K linear will be fine.
Breadboards:
I like the relatively small ones with ~300 connectors. Get a few and you can clip them together into a shape that suits your project. Some of these come with "power strips" built-in and with some you buy those separately. You don't have to have power rails on every breadboard as long as they all clip together.