First off, GOOD FOR YOU getting a roundpen!!!
Best training tool EVER!!! :)
Horses should be able to turn away or into you in a roundpen, depending on how you ask them or what you want. Both are valuable. Turning away helps with the hindquarters (someone already mentioned that) but turning in is also valuable because it teaches a horse to face you and listen solely to you.
Lunging is something that a lot of people think is easy but really it is the most complicated thing ever.
I have worked for a trainer for 8 months (had horses and showed for 18 years) and realized all this time I thought I knew how to lunge I really wasnt doing it right at all!
Lunging really comes down to one and 1/2 things: BODY POSITION, BODY POSITION, BODY POSITION.
And... voice commands.
Im not a Parelli fan at all (sorry in advance to those of you that are, remember we all have our own opinions) and I know he has countless videos on lunging but I wouldnt use them.
That being said, I always advocate for finding a respected trainer in your area that may be able to help and/or find some decent websites to read from.
A couple things I personlly would mention:
Ditch the lunge line. You are in a round pen. There is really no need for one.
Invest in a great lunge whip (most are about 10-15 dollars).
Go slow. Things don't happen overnight.
Become familiar with the drive line and concentrate on your body position.
KNOW WHAT YOU ARE DOING with your whip. A lot of people keep that thing raised high up which simply serves to either scare your horse into a run or desensitize them to the whip to the point that they wont move. When you want your horse to go, raise your whip slightly. When you get the gait you want lower your whip so you are draggin it on the ground.
I could go on and on, and I will try to find some articles I find worthwhile on the topic. If I do I will post them.
GOOD LUCK AND ENJOY YOUR NEW ROUND PEN!!!