I'd personally get something with at least 4GB of RAM, anything higher would be awesome. Intel i3 processors are generally okay for running games like RuneScape and doing everyday tasks, but if you can get an Intel i5 processor in your price range, that would be double awesome. You won't really need to worry about having a strong graphics card either. As for screen resolution, 1366x768 is typically standard on most laptops, but if you can score something with 1600x900 or even 1920x1080, you'll have a nice looking display.
Here's an example of something that's a pretty good bang for your buck (4GB Ram, 500GB HDD, Intel i3, 1920x1080 resolution for $370 USD):
http://www.amazon.com/Asus-F555LA-A...UTF8&qid=1464314861&sr=8-2&keywords=asus+f555
I'm biased and favor brands like Lenovo and Asus; just have had better luck with those brands then others. Find something similar or better then the one I linked and you should be golden. Feel free to PM me if you want my opinion on certain models. Cheers!