I disagree with the recommendation for the 135 f/2 - excellent lens, but on a crop it will be a bit long on occasion and it would burn up your entire budget. Instead ...
- Purchase the EF 85 f/1.8 ($359 today at B&H) - this will cover most of your fast lens indoor needs, and has excellent focus, and is very sharp. The AF will keep up with your sports and give you a fast lens for low light events like choir concerts where you might need the range.
- Purchase the EF 70-200 f/4L (non IS) $629 today at B&H. For outdoor sports, wildlife, etc. You don't need IS for sports because your shutter speed will need to be approx 1/500 and at that point IS isn't going to add value. This is one of the best value L lenses and one of the sharpest 70-200 lenses.
This is sound advice based on your budget, experience and camera body.
The 85mm on a Crop Sensor body works very well for Basketball, Volleyball, etc. On a Full Frame Camera I have found the 135 f2 the better choice.
The 70-200 f4L is a very good lens and will provide much improved clarity and sharpness and speed over the 55-250 (especially at the long end).
From the DigitalPicture.com: My recommendation is to get the Canon EF 70-200mm f/4 L USM Lens over the 55-250. I think you will appreciate the better image quality as well as the high end physical features - the extra cost is worth it in my opinion. The Canon EF 70-300mm f/4-5.6 IS USM Lens is also a better lens, but less definitively so. Though I don't think the Canon EF-S 55-250mm f/4-5.6 IS Lens is great in terms of image quality and features, we can't lose sight of the fact that it is very inexpensive IS tele-zoom Lens. There is a niche for this model. A casual shooter who is happy with their Canon EF-S 18-55mm II or 18-55 IS Lens and needs a tele-zoom for infrequent use could be happy with this lens.