...to increase your speed beyond a certain point, you will have to increase BOTH cadence and stride length -- this is because you can't endlessly increase your cadence, and so you will have to pick up the difference by playing with the other limiting factor to speed...
In fact, in Chi Running, once you find your sweet spot/cadence, you should learn to maintain it at all speeds. Even slow running. The change really does come from pushing out the back and swinging the leg through faster with more hip and knee flexion. Elite runners have a cadence of around 88 to 92.

So while we're on the subject, what else helps with either running or running stride? Are weights beneficial? What types of stretching is best?
The best type of warm-up includes dynamic activity that helps to stretch slightly while working on your own personal running faults. If you're a heel striker, marching is good with a focus on high knees and appropriate foot strike, then moving to skipping, then moving to bounding skipping where the focus is the slight forward lean of the body with the push coming out the back. Sustained stretches of tight muscles AFTER running (not before) is also helpful. Strengthening exercises are useful but that's getting really specific and what I would ask one athlete to do I may not ask of another, so I'm ot going there. If you're asking if using weight vests during running is helpful, I personally think it's rediculous.

In skipping, how do you prevent landing very hard - something my shins seem to dislike currently?
Start by just doing fast heel lifts with both feet on the ground. If that doesn't hurt, do it with one leg. If that doesn't hurt you can move to small skipping. The key to any of these is to work on rhythm, starting with slower movement and increasing quickness and foot position under the pelvis. It helps a lot to do it on a softer surface like grass.