One of the overarching factors that will affect your overall tone is the amp that you choose. Most electric guitar amp retailers can be extremely helpful in helping you find an amp that you like.
The first thing you need to determine when you are selecting an electric guitar amp is the style of music you intend to play. One of the best ways to select an amp is to find out what styles and brands your favorite musicians use.
There are two major classifications of electric guitar amps; Solid State or Tube. There are all kinds of variations around these two types of electric guitar amps. The longer and more often you play and experiment with different electric guitar amps, the more you will be able to notice subtle differences between the two amps. For example, Solid State electric guitar amps tend to clip (i.e. distort) after you turn the volume up past half to three quarters of the way. Tube electric guitar amps tend to get more distinct tonal characteristics as you play them longer and at higher volumes.
Here are a few major classifications that you can use to start.
Jazz: Fender Tube 'Silverface' amps
Rock: All kinds of variations, but generally tube half or full stacks
Metal: Most modern metal guitarists tend to like half or full stacks and especially rectifier guitar amps
Ultimately, the best thing to do is experiment. Try playing through a few different amps and see what you like. Do research on your favorite musicians and artists. Bring your guitar to the music shop and try every amp that you can. Just have fun!