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 1809, Build 17763
Travel is fatal to prejudice, bigotry, and narrow-mindedness, and many of our people need it sorely on these accounts. Broad, wholesome, charitable views of men and things cannot be acquired by vegetating in one little corner of the earth all one's lifetime.
~ Mark Twain