IMO this is the criteria you should be looking for:
Intel Core i3/i5/i7 3xxx or 4xxx series processor with a speed at or above 3.0ghz, core i5 4460 or higher preferred
8GB of RAM, more is fine but you won't notice the difference above 8
At least 6 USB ports, at least 2 of them should be blue USB 3.0 ports
Unless you want to do 3D gaming or you're going to be watching 4k video there's no need for dedicated graphics
If I were buying for a family member to surf and multitask without any gaming needs, I'd get this computer and add a 64-128GB SSD to it:
http://www.newegg.com/Product/Product.aspx?Item=N82E16883220694http://www.amazon.com/dp/B00LX7LUU8/Then you'll want a monitor of at least 22" and 1920x1080 resolution that takes an HDMI input. I prefer 24" and IPS type screens.