To add to what
@Rick P has already said, sometimes the best way to learn correctly is to learn how to play cleanly (e.g. hear each note clearly without fret buzz unless intentionally muted as such).
There are numerous amps which sport cascading preamp channels which increase the level of overdrive or distortion (distortion is actually described in layman's terms as overdrive pushed further which becomes distortion).
If perhaps you'd like to learn from the best examples of how overdrive is used, listen to either Larry Carlton or Robben Ford's releases. Both use high quality amps that capture overdrive in its most discerning forms.
In one of Larry's instructional videos, Larry describes how he utilizes overdrive as tube saturation just at or slightly beyond the point of "break-up." The key is to turn your guitar volume to about 5, ands increase your amp's volume knob to about 3 -½ or 4. Your amp's master volume should be so that it won't disturb the neighbors or housemates.
At 3-½ or 4 your ears should hear where the amp begins to sing like classical stringed instruments might sound. If the amp volume is correct, your guitar will sing like a viola or violin. This is Larry's preferred amp tone which he has used on countless songs and performances. By simply hitting the strings harder, or by slightly increasing the guitar volume, you can push this tone into further overdrive where "grittier" distorted tones exist, or by rolling back on your guitar volume, "clean up the tone" for quieter clean tones.
However, if perhaps you are younger, you may feel the need to use overdrive and distortion freely. (Let it be known that distortion covers a multitude of playing errors by masking misplayed notes or chords. Also let it be known that the most experienced guitarists learn how to play their notes cleanly and then embellish their tone with overdrive and distortion after-the-fact.)
In time, you'll know what to listen for in amps; the EQ response, the dynamics, the warmth vs brightness. You'll know what tubes produce what type of tone, you'll also know what type of speakers produce what types of tone. And lastly, you'll find that you'll likely never quite be satisfied for any great length of time with one particular amp or tone. As you grow older, your music tastes will also change over time.
For example, when I was 17 years old, I thought the massive tone of Pete Townshend's SG through a HiWatt amp on "Live at Leeds" cranked through my the stereo was THE tone. As time went on, my choice of tone changed as well. I became more docile.
I currently use a modeling device (HeadRush Gigboard) and stereo FRFR108 powered speakers for its versatility, adaptability, and range of amp tones. Not to say that my youth was not a lot of negative emotions bubbling over on a hot stove. (In reality, yes, this) What I learned was how to use self-control in a way made me a stronger individual. It also helped me find peace within myself.
Anyway, my hope is that like many others who have come before you, you will also join us on your personal journey of growing and learning, your personal journey of discovery of what choices and steps you can take that will result in good things for you.
Because amp and effect choices are widely subjective, my only advice is, be open to listen to new tones and concepts. Ultimately, your ears will decide for you what you like and what you don't. And since there is a lot being offered of what we don't like, it makes sense to be discerning so you'll know what you will like, versus just accepting mediocre tone you'll not enjoy for a length of time. Enjoy the ride, but know when to settle down on what you've found that you like.
