Distortion is the one effect absolutely necessary for rock guitar. Nowadays most amps have it built in - called variously gain, distortion, pre, drive, overdrive, o/d, etc etc. Also available in 'stompbox', it comes in different flavours, viz.
Fuzz - buzzy, sizzly, farty 'Satisfaction' tone, think Hendrix 'House Burning Down'. Good example - ElectroHarmonix Big Muff Pi.
Overdrive - warmer, less radical distortion, intended to mimic the sound of overloaded valves - think Stevie Ray Vaughan. Good example - Ibanez Tube Screamer.
Distortion - generally somewhere between fuzz and overdrive, intended to mimic flat out valves - think Joe Satriani. Good example - Boss Turbo Distortion.
Metal Distortion - heavy distortion with 'scooped' EQ - less middle, more bass and treble - think Metallica. Good example - Boss Metal Zone.
Multieffects have come on in leaps and bounds in the last few years, and are good value for money, as they include distortion, delay, reverb, chorus, flange, wah etc etc all in one box. Because the rate of progress is so fast, they lose their value very quickly (like any computer technology) - but this does mean that older models can be picked up very cheaply. Try Korg, Boss, Zoom and Digitech. Do remember, however, that they can't compensate for a lousy amplifier - whereas if you get a good amp, you may not need effects at all. Also, don't be dazzled by 3001 different multieffect sounds in the shop - 2 really good sounds (1 clean, 1 distortion) are all you need.
Alternatively, go for a couple of good stomp boxes - distortion, wah and delay being the most useful.
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