Hey, another drummer! greetings from your transatlantic cousin.
I've owned several acoustic drumkits over the past (one of which was a beautiful massive maple kit with 24" bass drum, and 14", 16", and 18" toms), forever, and i currently own an electric kit (a
TD-9S).
What is your budget? I understand that you might not know how much your parents will contribute, but it's nice to have an amount you're willing to spend, so you can find the best for that amount.
I'm not as familiar with the brands outside of america, but i can tell you the basics to look for.
There are four kinds of wood usually used in making drums (though there are many unique woods used in minorities). you can read about them here
http://www.drumthunder.com/drum-set-wood-types/
For you i would probably recommend a
birch or mahogany kit. They're pretty cheap, but not so cheap that they don't come with nice hardware (cymbal stands, etc). AND, they would fit the music style you want to play (punk).
Really though, 90% of a drum kit is in the heads you put on it, i have seen crappy kits that sound 100x better than expensive kits because they had nicer heads and were tuned properly.
So the problem with getting a "starter" kit isn't necessarily the basswood, as it can be made to sound great! It's the cheap hardware that comes with it. And if you want to gig with it, you will not want flimsy light hardware that falls over all the time and is likely to break. The set that you posted a link to seems to be on the flimsy side to be honest with you. That and it doesn't come with a ride, which means you would have to invest more money on that. (assuming you aren't planning to just buy a set of nicer cymbals).
I think that if you bought that set you would be disappointed. Especially with the crash cymbal.
If you can you could go to local shops and try out some different sets to see what you like, and then find it online for a cheaper price.
One man, one lawnmower, plenty of angry groundhogs.
