You might want to try a 12 Volt DC bulb for a car turn signal. That gives off a lot more light than a candle.
You can use a simple logic-level transistor (like a TIP120) to vary the bulb's brightness. Just hook the base of the transistor up to a PWM output pin of the Arduino and use an analogWrite command to set the brightness of the bulb.
You will probably want a 12 Volt DC power supply (although even 5 Volts gives reasonable brightness), but it's pretty easy to find 12 Volt wall warts.
Using a bulb like that will probably be safer and easier than using a bulb designed for mains power. As has been pointed out, that's not something you want to fool with when you are first starting out.