The basic effects boxes include the distortion and the "wah-wah". The single effects box is literally a box with a little pedal on it. The pedal acts as the on/off switch. For instance, with a distortion box, you can step on the pedal to switch to a distorted electric guitar sound during a chorus, and step on the pedal again to switch to a clean sound after the chorus and at the start of the verse.
The distortion effect is used in every rock song made. There are just a lot of variations on it due to artistic differences. For instance, the guitar effects used by Breaking Benjamin would be a really thick distortion so it can be maintained even when they just pluck through individual bass strings. Three Days Grace, on the other hand, use a thinner distorted effect because the guitarists riff all the time. While they have different effects, both work wonderfully with their songs.
The wah-wah pedal is often used in reggae and similar incarnations, such as ska. This pedal is usually hooked up with other single-piece effects boxes, as it simply produces a wah-wah sound. Stepping on the pedal "bends" the sound on the guitar and makes it "talk" with "wah".
Guitarists who know their effects only usually purchase single boxes and make a mini-circuit out of them. They put them in a piece of board and interconnect each and every piece of box. If you are just learning your effects, you might want to go for a multi-effects box instead. This way, you can learn how to mix your own effects. Multi-effects boxes also allow you to quickly change effects at a press of a button; which is handy if you handle riffs and solos and other responsibilities in your band.
When you buy electric guitars, keep in mind that you will need to get an effects box. Electric guitars don't really sound good on their own, and an effect to the sound can give that extra "oomph" to the songs that you play.