Hey Taylor, first off, it's a pretty big misnomer that the quality of camera will immediately improve your photos, or a certain type of camera takes better photos than others. While it may be slightly true if you start pixel peeping, cameras are more about performance and lenses are more about image quality. So if you want good, high quality images, lenses are usually a better investment per dollar. That said, the camera you got is a great body and performs very very well...you made a good choice. Skip already made a recommendation on a lens which is a pretty good bang for your buck, but with a crop sensor camera like yours the effective focal length is now 50mm x 1.6 = 80mm. 80mm is far too long to get good wide structure shots if that is what you want to take. It would be good, though, for tornado shots that you're not directly under the rotation. I personally prefer wide-angle zoom lenses while I'm chasing (and really for everything else) since you can go super wide to get a massive structure shot or zoom in slightly to get a closer view of an updraft or tube. Some excellent lens choices for your camera are the Canon 10-22mm, Tokina 12-24mm, or even the Canon 17-40mm or 17-55mm IS if you want to pay a bit more money.
But now on to your original question. Personally, I always shoot in either Aperture Priority or Manual mode...usually Aperture Priority unless have I time to compose and exposure a proper shot. I like to be able to control the aperture which will affect the sharpness and depth of field of focus. A larger aperture (smaller f/ number) will mean a faster shutter speed since you're letting more light in but less depth of focus and most lenses won't be quite as sharp wide open. A smaller aperture will mean a slower speed but usually a sharper image and more depth of field.
As for ISO speed, if I am on a tripod I will typically set it to 200 unless I need a faster shutter speed for some reason. If I'm shooting freehand, I'll typically turn it up to 400 or even 800 if my shutter speed gets too low. In storm photography, noise if often accentuated in the dark areas of storm clouds, so even though you may only be shooting at ISO 400, if your clouds are underexposed the noise will appear much worse. And since I already mentioned it, if time allows during your chases, GET A GOOD TRIPOD! There is absolutely nothing that affects the quality of your photos more than a tripod. You can always tell which people are serious about getting good photos and which people don't know what they're doing by the size of their tripod [insert joke here]. I realize that often times in storm photography a tripod is a luxury that often can't be taken out, but it never hurts to have a good solid one along.
Another good suggestion from Skip is to shoot RAW. It will take some time to learn to process correctly but you'll have so much more freedom and information available to you in the image that your image quality will improve drastically once you get the hang of it.
The final piece of advise is to simply get to know your equipment well. Get to know which buttons do what and what affect different settings have on your photos. When the shot of a lifetime comes along you should be able to switch settings on your rig without even looking at them.
Oh yeah I almost forgot the most important part: don't forget to have fun. It's a learning experience and one of the most rewarding things you can do.
