Biggest tip I can give you, as others have already said, is go SLOW.
Another bit of advice is to not always expect positive results from her (that's just not always going to happen), but do always end the lesson on a positive note. Also, it is a very common training trend for a horse to learn by leaps and bounds, and then all of a sudden weeks later act like your've never taught them a thing. Don't get discouraged if that happens, as it probably will. That's just the learning curve for horses.
Always ask for baby steps first, before expecting big correct responses. For example, if you got on her saddled for the very first time and want to ask her to walk while being ridden (of course, we've prepared her on the ground first before this point), she probably won't know what to do when you apply pressure to her sides to ask her to walk. The very instant she takes a teeny step forward with any of her legs, you need to stop the leg pressure as her reward. And allow her to stand and rest. That's the tiny baby steps. Once she is consistent with taking a teeny step when you ask her to go forward, do not release the pressure of your legs until she gives you one normal size step. Again, keep working on that until she is consistent. Then start asking for two normal sized steps. And so on. This may take one minute or it may take 30 minutes. All horses learn differently. But that's the point of training in baby steps.
And that also points out always ending the lesson on a positive note. If you apply leg pressure to ask her to go forward, NEVER release that pressure until she responds correctly, even if it is the smallest response of a forward step. For teaching some things, you may literally have to hold your cue steady for minutes, until you get a correct response. But when the horse does give you the right answer, you need to immediately stop asking and release the pressure (which is their reward).
Definitely get in as many training sessions as you can with an actual trainer who has started a young horse before.
As far as the lunging, a round pen is not necessary at all. Yes, it is easier, but I think every horse should be able to be free lunged. It's just another training tool and training lesson. When I lunge a horse, I basically just use the lunge line and a long lunge whip. I never need to actually "whip" the horse, but the whip serves as making my arm longer. I can point it at their shoulder if they need to move out and make the circle larger. I can wave it at their hindquarters if I want them to speed up. I can move it in front of them so they turn around to go the other way on the line (always putting their hindquarters away from me on the outside of the circle. It's a respect issue. You never allow your horse to turn their hindquarters toward you.). Make sure you keep your body positioned behind their midline, if you want them to continue to move forward. If you want them to stop or to turn, then you step so you are in front of their midline. Body position is key, to lunging.
Make sure you start with a small lunging circle at the walk, to train her to free lunge first. Once you can do that, then you can work on making your circle larger while still being in control, at all gaits.
∞•*˚ Βгįťţαňγ ˚*•∞
It is not enough to know how to ride; one must know how to fall.