Using an RPi3, Raspbian, /root moved to a USB-SSD and lxde replaced with xfce, "Iceweenie"* is an acceptable browser for most websites. I have used this combination as a general purpose browsing desktop for some time with decent results. I wish Raspbian would follow the examples of the Ubuntu Mate RPi distro and Arnie Exton's ArchPi and include access to Firefox. Alas, it is chained to Deb Jessie.
I have used Firefox Sync to transfer all my preferences, bookmarks and history to the Iceweenie on my RPi3 and the memory loading does not seem excessive according to Htop. You do not want to open too many tabs though or the memory load will be too much but it is much more satisfactory than the cr*p-ware Epiphany that seems to crash randomly and for no apparent reason.
I do not recommend using the lame-*ssed wifi on the RPi3 board for such web intensive applications unless you are right next to the router or AP. The puny chip antenna just does not cut it. Size really does matter, especially with uWave RF. They would have been better off to just leave it off, or charge a buck more and put the uFL connector on. I am currently awaiting the arrival of some uFL connectors to solder on the bottom side, remove the chip and put a real antenna on it. Ethernet is the only long range solution for now.
* My irreverent renaming of "Iceweasel"