Some common mistakes made by new players including myself are limping into way too many pots pre-flop, ignoring the ramifications of position, and overvaluing mediocre hands such as KT, QJ, A5, etc.
Also, you should get started as soon as possible on learning how to count outs and calculate pot odds
, because you cannot advance to any decent level without these skills. Being able to do these calculations will help keep you from constantly losing chips by calling off your stack chasing draws without the proper odds, for example.
I chose to focus on tournaments starting out because I could play in freerolls
and practice the basics without worrying about spewing money. I'm not aware of any particular advantage in starting with tourneys over cash games, beyond being able to experience many more hands with your losses limited to just the buy-in.