1. You should be able to look up the rodeo online and find info about the location. It's very important to know if it's a covered or enclosed arena or not. If it's covered, chances are that you'll have a tough time shooting anything with a kit lens. Really dark arenas it's hard to get much even with f2.8 lenses.
Outdoors under an overcast sky is ideal lighting. If it's sunny, you'll have heavy shadows and most rodeo competitors wear wide brimmed hats... A fill flash is one recourse. But you'll need a fairly powerful one such as a 430EX or 580EX. The built in flash is no where near powerful enough and it's in the worst possible place for causing nasty eyeshine, anyway.
Heavy Photoshop post-processing is an alternative to flash, or might be needed in addition to flash. Be very careful not to under-expose and shoot RAW in order to have the most flexibility working with the images after the fact.
If indoors or covered, they might use rather nasty sodium vapor or mecury vapor lamps. If it's the primary light source, set a custom color balance or you'll have a difficult time adjusting it later in post processing.
You also might find a mix of light types... indirect sunlight from the sides, skylights which are usually yellowed with age and dirt, and sodium/mercury vapor. That's a really tough situation and takes some extensive post production work... or convert your images to black and white. I usually ask venues to turn off sodium/mercury vapor lamps when there's a mix with indirect daylight. Most cooperate.
2. Flash doesn't scare horses unless you're really close and it goes off right in their face or they can hear it "pop" and recycling. Otherwise, it's just like lightning or reflection off a car window or water, and they tend to ignore it. Particularly if you are using fill flash, as opposed to full flash. Young or "green" inexperienced horses I watch out using flash, they might react to it. Try setting off the flash from a reasonable distance, with it pointed toward the ground and watch for their reaction. If they seem nervous, don't use it. But most will completely ignore it so long as you are at a reasonable difference.
The best way to avoid eyeshine is to get the flash off-camera, on a bracket to the side and well above, away from the lens axis. Eyeshine is worse indoors, when animals' eyes are dilated in low light, than it is outdoors in strong sunlight.
In a competitive situation you might not be allowed to use flash. At a rodeo it's probably not a problem, but you should check with the organizer and venue to be sure.
3. There is absolutely no way I'd give my shots away to a newspaper. They can pay for any shots they want to use. It's horrible precedent to start giving your shots away to them. Photo credit is worth absolutely nothing. You can use the shots in your design portfolio whether the newspaper publishes them or not. Find out what they pay their stringers or spend on stock photos, then dont settle for anything less.
4. If the newspaper "hires you" for the rodeo (or any other assignment), be very very careful. Chances are they will end up owning your photos, you'll be giving up the copyright and they will have the right to sell the images to other newspapers and publications via the wire services. Not a good thing! If you're job description at the newspaper doesn't mention anything about taking photographs, that's good and you should negotiate separately for any usages... But if your job description mentions it, any shots you take they can end up owning and you should get something in writing spelling out that your shots taken outside the work are your own. A friend of mine worked for AP as a staff photographer for ten years... He still occasionally sees his shots in stock libraries... They are still selling them. He doesn't own any of them and has to ask permission to use his own shots in his portfolio!
Edit... okay, it's outdoors... Good. Now you have a choice of working the light or adding your own, if it's sunny. Or a little of both. By working the light, I mean moving around so that the sun is at your back. Of course, midday that's impossible and when you'll most likely need fill flash. Pray for high overcast... that's the best lighting.
Keep your shutter speeds up... It takes 1/500 or faster shutter speeds to freeze a galloping horse. Even faster would be better. You might get blurred hooves at 1/640 or slower. Of course, you can do some interesting panning shots and deliberately include motion blur, too. You'll throw away a lot of those, but when they work panned shots can be pretty cool. Experiment a little with slower shutter speeds and panning.
Try to work from right beside the arena, if possible. It's neat to shoot from down low, but you have to be careful about startling horses. They might think you are hiding and getting ready to jump out. It's best to be in plain site, so that they can see and easily recognize you as a human being. Some horses get nervous when you point a camera at them, but not so much if you are a reasonable distance away.
Use just the center AF point and set your camera to AI Servo, to track moving subjects. I suggest thinking about using Back Button Focusing
, too. It's a good technique to learn, with any kind of action photography. Practice tracking moving subjects with the center AF point, just to get the feel for it... maybe cars on the street or something like that.
You should have no problem using ISO 1600 on your camera, if needed. Outdoors in sunlight you can probably use a lot lower... maybe ISO 400. Use the exposure method of your choice. I use M if the lighting is steady. That makes for a lot less adjusting and correcting after the fact. But if you are used to shooting in manual mode, then the auto modes of Av, Tv or even P can be used... just watch that your shutter speeds don't get too slow.
