Aerobic fitness is what you want, but strength is also essential. If you are strong then each contraction of your muscles is worth more, so increases your power overall. However don't do too much strength training, as it will then start to convert your fast-oxidative glycolitic (FOG) fibres to those of a strength athlete.
Aerobic fitness will give you the ability to keep going and going. Your aerobic system can provide power for as long as you have the food and oxygen for it (basically indefinitely), but doesn't provide much energy per contraction. Therefore for very fast and very hard actions, such as jumping high, sprinting, punching, etc, you need strength above fitness. Look at Linford Christie for example - he has the bulk of a bodybuilder and needs it to run so fast. However he could not run very far as he relies on his ATP-PC and anaerobic glycolitic systems for energy, which while they give a lot of power, will run out very quickly (ATP-PC after about 10s of use).
You need to decide just which of these two you need to be. You cannot excel at both, because of your FOG fibres. However both routines need elements of the other. If you choose to become an aerobic athlete, do a lot of very slow jogging, and supplement this with a little strength training, and a fair bit of intervals training (this is a special kind of running that increases your anaerobic threshold, or AT, which put simply enables you to run faster without using anaerobic systems, which of course will run out and also give you loads of lactic acid in your legs, which won't help at all). If you're a strength athlete, do loads of strength training, but don't forget to do a bit of running too. Also do plenty of sprint training. And stretch, warm up and warm down before and after every single activity, unless it is a very slow jog.
One thing that may influence your decision of which to be is what's known as your somatype, which is one of three different types of build. You get Endomorphs, Mesomorphs and Ectomorphs. The first two may as well be the same, as today when we all have a little too much fat on us there is little to distinguish. Basically, if you are an ectomorph, you are tall and skinny, and have narrow shoulders. I'm one of these, and it means you'll do very well as an aerobic athlete. If you're not, you'd do better as a strength athlete. Of course it isn't as concrete as this, it's not like being male or female, and there are people at Olympic level who have the "wrong" somatype - but it may help you all the same.
If you've any questions don't hesitate to PM me
Chris