Feedly is an aggregator wherein you select your own sources and it pulls articles from them as they publish. I’ve used it for a long time and like it.
As do I. Very, very powerful tool.
Here's a screenshot of part of my Feedly feeds:
It allows you to capture RSS feeds from multiple sources as well as supporting customized searches.
For example, I can enter this search pattern
And, not only will I get the search results, but it will keep collecting articles that have those three words in them.
Since you're sick of Drudge, one thing that I recommend is keep Drudge's RSS feed in Feedly and I can go straight to the articles he links without having to deal with the ads on his page.