For the kind of pictures I take, honestly I never really use image stabilization. If your Shutter speed is high enough it isn't necessarily needed. A basic rule of thumb is your shutter speed should be at least equal to your focal length...so if your zoomed all the way out to 200mm, than your SS should be 1/200 or higher. Now if your shooting action your going to at the very least need 1/500 if not higher. Now image stabilization is only going to compensate for hand shake and its not going to stop the action.
That lens you picked out will def work. Sigmas HSM focusing is pretty good but there is a lot of range in a cheap price, that's not necessarily a good thing. The reviews seem pretty favorable so it might be worth trying.
Heres what I would recommend. Look for this lenses in your local craigslist.
first would be a Canon 28-135 f/3.5-5.6
http://www.bhphotovideo.com/c/product/149629-USA/Canon_2562A002AA_EF_28_135mm_f_3_5_5_6_IS.html
This is a kit lens that people generally get with 50d and 7d..usually these go on CL for around 250-300. Its a great all purpose lens. Will perform way better than the sigma (remember you can always crop pictures)
next is the 50mm 1.8
http://www.bhphotovideo.com/c/product/12142-USA/Canon_2514A002_Normal_EF_50mm_f_1_8.html
this is a great budget lens, often referred to as the "nifty fifty" great for portraits and has a huge aperture. Just read the reviews! It usually goes for 60-80 bux on CL.
I know the next one is a lil out of the price range you stated, but this lens is the cheapest of the L series, and one of the funnest lenses I have ever owned. Its the 70-200 F4L
http://www.bhphotovideo.com/c/product/183198-USA/Canon_2578A002_EF_70_200mm_f_4L_USM.html
This lens is great, perfect range, constant F4L throughout the whole focal length, lightning fast focusing and cream of the crop Canon L quality. This lens is perfect for action photography. They pop up on CL all the time for around 500 bucks used (the image stabilized version is a tad more so don't get them confused)..I bought mine used for 500 bucks, used it for 2 years and sold it on CL for 500 bucks! L quality lenses hold their value!