Choosing an Amp
The main things to consider when choosing an amp are price, your core tone desired, versatility, reliability, and power. Most amps are designed for one or two types of tones and have a tonal signature that is difficult to find elsewhere.
The modern amplifier generally has 2 to 4 channels that you can switch between. This will give you that many distinct tones. Some amps have completely independent controls for each channel, while some amps share some controls across channels which may make them less versatile. Beyond that, some amps have controls that affect all the channels.
Contents
Overview of Common Channels
Clean
Clean channels are designed to get a relatively clean (undistorted) tone. That being said, some amps' clean channel is still a bit dirty. Sometimes this channel will feature a gain control to dial in pristine cleans vs. mild crunch, but usually not. Even if there is no dedicated gain control, it may still be possible to push the channel into distortion by maxing out the available EQ and channel volume controls.
Simply because tones are clean doesn't mean they'll sound identical across amps. Some amps will have a more compressed sound than others, or have more sag or otherwise alter the attack of the inbound guitar signal. This can get very complex, with the compression affecting some frequencies more than others. Some amps are known to be "warm" while others "sharp" or "cold".
Its also important to pay attention to the tone of the notes as they sustain. Some amps are said to be "organic", while others are "sterile".
Crunch
Crunch is basically a mild to strong distortion, but it usually responds more to attack and playing dynamics than a lead distortion. This channel usually has a dedicated gain control. At lower levels, it will sound like a dirty clean channel. At higher levels, it has a fairly saturated distortion; however, the breakup tends to be a bit noisier or harsher than a lead channel's. In other words, it is less compressed and dirtier than the lead channel, but more compressed and distorted than the clean channel. The distortion also tends to sound more nasal and vintage than modern and tight.
Lead
The lead channel offers you the maximum amount of gain and the most modern tone. The response is tight and the distortion can get very saturated while remaining fairly smooth and harmonic. While it's typically labeled Lead, this channel works well for both leads and distorted rhythm where heavy distortion is preferred over prominent attack. It will almost always have a dedicated gain control to dial in the desired amount of distortion and sometimes has additional tone-shaping controls that other channels don't.
Lead 2
An additional lead channel may simply offer more versatility by being a complete duplicate of the other lead channel or have a different signature to the tone.