The best streaming services for both sports and news channels are Sling TV, Fubo, DirecTV Stream, Hulu with Live TV.
The cheapest way to get news and sports is Sling Orange for $35/month, which has all the ESPN channels for sports and BBC America, Bloomberg, CNN, and Newsy for news. That's tough to beat.
The second best option is getting Sling TV Orange + Blue, which also gives you the NBC and Fox channels for $50. The other streaming services cost between $64.99 and $69.99.