Disclaimer: I don't throw amazing drives. My max is about 300 but that is only with absolutely perfect form and snap which I am not consistent with yet. I probably more often throw about 220-260.
That being said, my advice to all of my friends that are just starting out is to ditch the name "run up" and call it "footwork" instead. The name "run up" implies that you should be running, which I strongly discourage for newbies. If you have been playing for years and have the mechanics and muscle memory down then feel free to actually run. I think newbies should slow down as it will help them solidify the rest of the mechanics.
In fact, I was in a slump lately and for several rounds couldn't figure out what I was doing wrong. I eventually slowed down and VIOLA! My drives instantly got better. Why? I believe that subconsciously I was expecting the momentum of my body to somehow propel the disc and thus I failed to snap it out of my hand. Also I believe that I was neglecting to really pull the disc across my body, and failing to focus on weight transfer. Both of these led to throws with less than optimal rotation on the disc. Obviously, both my accuracy and my distance were abysmal because of this.
I would say the point of footwork is to get your body into the optimal position to really launch the disc. Even stepping at a slow speed (I do a cross-step in my footwork) will help you turn/reach back further, and spin your hips better. It also allows for a great shift in your body weight so that you're not throwing off of your back foot.
In realty they say that everything is about "Location! Location! Location!" but in disc golf it's all about "Rotation! Rotation! Rotation!" The more you can impart spin on that disc, the better it will do what it was designed to do.
My advice to some newbies that I have played with lately for driving:
1. WALK don't run
2. Keep the disc close to your body -- release more like you're pulling a cord to start a mower straight across your chest rather than some swooping, circular motion far away from your chest
3. Throw when your weight is centered, or just at the point that you are leaning to your front foot. Do not throw with your weight on your back foot.
4. Pull the disc back across your chest, not down at your waist. This allows for a more level release. If you are pulling it back at waist level then the natural follow-through in your arm will be an upward motion, essentially forcing a high, hyzer shot. Doing this is bad form as your discs will basically just go high into the air, fade hard, and will not travel very far. Of course if you intend to hyzer up and over some trees then pulling back low is what you want! For a nice, even release -- intended for maximum distance regardless of height -- you don't want a really low pullback.
5. Don't try to overpower the disc. Just make sure to SNAP it out at the very end and let the disc do the work. Your arm shouldn't be sore after playing one round or you are trying too hard. It's better to snap the disc for maximum rotation than to try and "push" the disc through the air.