I would just go AMD Ryzen if I was you. Ram and cpu play a huge part in overall computer performance nowadays. DDR4 ram is still expensive, but if you Craigslist shop, you can save a bundle and have a fairly good PC. Don't worry too much about power consumption, at idle modern GPU's/CPU's downclock to very low frequencies and draw extremely little power.
I know this is just for web stuff, but I recently built my parents a new computer(Ryzen 5 1600) (albeit, theirs was 1400$) and their computer was only 4 years old (AMD bulldozer). It has been 3 weeks and I still get the occasional 'This thing is so much faster' texts from dear old mom. All she does is web browsing, YouTube and Facebook. (the expense part of it is because my youngest brother wants to play video games).
__________________
|