Pickup type is all about the tone of the sound rather than skill level. Meaning there isn't an introductory pickup type.
In terms of puck rock you could go either way re. humbucker versus single coil. In The Clash Joe Strummer played a Telecaster with single coil pickups and Mick Jones played a Les Paul with humbuckers. One band using both of the classic pickup configurations.
The body type matters too.
Heavy body with humbuckers, the classic Les Paul, has characteristic sustain and deeper, bass sound. Lighter body with single coil, the classic Fender types Stratocaster or Telecaster, has a lighter sound.
If you play with a clean sound, the difference will be noticeable. If you use a lot of effects you can dramatically change the tone away from the characteristic tone.
You can also split the difference and buy a model with both single coil and humbucker. That is a common option.
One last point of detail...
...combination HH, but I heard it and it sounds like distorted
It won't be distorted unless you overdrive the amp or use a distortion effect and this is the case for either humbucker or single coil pickups.