I'd go with either reading RSS or using the Twitter API to follow sport news accounts. (I don't know of any specific dedicated sports accounts on Twitter, but I'm sure there are several similar to
http://twitter.com/cnnbrk with sports news, scores, etc.)
RSS has the advantage that you'll generally get a headline/title and either partial or full body content from the feed, but the disadvantage that some feeds contain partial body content and others contain the full body. If you want to display the content on your site, you'll need to check the feed's licensing terms to avoid copyright problems and, even if it is allowed, you'll need to work up some code to retrieve full bodies for any feeds which only contain partial content. You can sidestep these issues by just putting the headlines on your site and linking to the original source.
Twitter has the advantage of consistency - it will always be just the headline and a (usually bit.ly shortened) link - and the disadvantage that longer headlines will be cut off by the 140-character limit. It avoids the licensing and partial-vs-full content issues by only providing you with a link to the original source and no body content.
Having done both in the past (scraping RSS feeds for
http://seethefnews.com/ (Warning: Extremely slow site!) and filtering Twitter for
http://fishtwits.com/), I would personally go with Twitter. It's a lot easier and avoids having to do feed-specific coding to deal with various publishers' quirks. Plus Twitter's all trendy and everything right now, so it could score you some cool points with certain people.
