I can't speak to media hosts, but as a former broadcaster, traditional and web-based (I started in 1997 with the Progressive Networks Player, the precursor to the Real Player) the equipment is key. You don't need to go crazy but the better the camera to capture the action the better the stream will be.
Depending on your budget get a nice digital camcorder. An HD camcorder may sound like over kill, but again, best in best out. And HD cams are relatively cheap (especially compared to when I was still in broadcasting).
Same thing with audio, get a nice quality mic and plug straight in to the camera to get the best audio.
Webcams are great these days, and very budget friendly, but you might not get the image or audio you want from a sporting event with one.
If it were me I'd call B&H Photo Video here in NYC. Tell them what you are trying to do and what budget you have and they are great setting something up (I've spent a $100 there, I've spend $40,000 there, always helpful and always able to get me the most bang for my buck).
Those few basic items are roughly $1,000. That leaves the extra $1,000 for memory cards, extra microphones (maybe a wireless option), maybe a small mixer ( http://www.bhphotovideo.com/c/product/601120-REG/Peavey_00512000_PV... ) if you want to use more than 1 mic at a time, extra batteries, extra cables, $$$$ for a streaming host, basic video editing software (iMovie is free if you're Mac based, Final Cut is better but costs a few hundred) etc...
Poking around B&H got me all nostalgic for my broadcast days, I loved shooting & editing video....
If this is for a school, check into ihigh.com. Not only free, but you can actually make money. Not sure if it's popular all over the country, but in the midwest, almost every high school is on it. Easy to setup, easy to run. Equipment can just be a firewire camcorder, or if you can use a $100 device that converts video to usb.