The latest browser I can think of that should still support your OS and still gets updates (for a few more months at least) is the extended support release of Firefox 45: https://www.mozilla.org/en-US/firefox/organizations/all/ While it may not support the latest HTML5 features, you'll still be patched against security vulnerabilities.

Alternatively, you could install Windows 10 using bootcamp according to the bottom post of this thread: https://discussions.apple.com/thread/7171259?tstart=0 Windows 10 works pretty decent on low RAM devices, and you'll be able to run all the latest browsers and software.