How to do a good purchase online?

I have a mastercard card and I want to start purchasing clothes and stuff online from stores that we don’t have in Iceland or Denmark or something like that. I was checking on ASOS and saw there was a disscount going on so I checked out the clothes and I really liked them. I have never done it before, my parents say I can be hacked and stuff like that, I was also looking for an iphone or side-kick from ebay, but am scared of being hacked.
What do you suggest?
I want it to be perfect, is the shipping expensive?
Basically you could just give me some advice and what to look out for and stuff like that.

All your help is much appreciated!