A very basic explanation of the numbers, from one beginner to another.. The f numbers refer the the minimum aperture settings of the lens. The lower the f number, the faster the lens. The faster the lens, the better it will perform in low light.
So, for example, the nifty fifty (f/1.8 50mm) has a focal length of 50mm and a minimum aperture speed of 1.8 - So it's great in low light, because it's quite a fast lens. Prime lenses tend to be faster than zoom lenses, because there are less necessary obstructions inside to block the light.
So, lens choice would be based on what you're hoping to do with it. In your case, you're outside shooting events, mostly, so a very fast lens isn't really a necessity (as there is plenty of available light); Depending on how far away you are, you might want a lens that can zoom quite far, or if you're closer, perhaps a shorter range lens that may give a sharper pic. As far as focal lengths go, there's wide angle (around 8mm-20+mm), standard zoom (20+mm-70mm) and long range (70mm-500+mm). You'd probably be wanting a prime or a standard zoom lens in the mid range.. So the 55-250 that has already been mentioned would be a good call.. Or the new IS version of the kit lens (18-55) (bearing in mind that IS isn't going to be much use if you're panning..) OR the 17-55 (although that might be getting a bit too far towards the expensive side of things..)
Note: I'm a beginner at this myself and I'm still learning, so the experts on the forum will probably be able to assist further, and correct all the mistakes I no doubt just made in the above explanations
I've tried to simplify the number, so apologies if I've oversimplified anything.
Hope this helps!