Now I will start with the least-sexy of effects, but the most useful: Compression.
Compression is used to shape the sound. It can alter the attack. It can add sustain. It can level a signal. And it can take years to truly learn. However, when you hear a clean guitar on a coffee commercial and wonder why it has such fullness and why each note is ringing clearly into each other, it isn't because it's a vintage Strat. It's because the attack on the compressor is set to allow the attack of each note to be heard and the release is set to allow for sustain.
Want to sound like David Gilmour? You will need one. For distortion, it is less noticeable, due to the natural compression of a distorted signal. However, it can add more sustain.
The next-most-useful effect will a distortion effect. By that I mean a fuzz box, distortion box, overdrive, tube saturator, pixellator or even a ring modulator!