Definitely don't rule out manufacturer refurbished units if you need a higher spec box than you could afford if buying "brand new."
Given your usage notes virtually any true laptop (not netbook or Chromebook) you can buy that has a processor above the Celeron (which is most of them) will be a major improvement over what you have.
In AMD processors an AMD-A8 or higher (A10, A12) APU would be a significant improvement over what you have as well. I have AMD APU machines, one A6, one A8, and two A12, and all still work. I needed "higher horsepower" than the A6 and A8 were capable of, so I replaced both with A12 machines, though both work just fine, and quite quickly, for basic web browsing and office suite work.
Brian AKA Bri the Tech Guy (website in my user profile) - Windows 10 Home, 64-Bit, Version 1803, Build 17134
. . . the presumption of innocence, while essential in the legal realm, does not mean the elimination of common sense outside it. The willing suspension of disbelief has its limits, or should.
~ Ruth Marcus, November 10, 2017, in Washington Post article, Bannon is right: It’s no coincidence The Post broke the Moore story