The system has only 2 GB of soldered RAM and can't be upgraded. It is a Intel Celeron processor. A similar system works fine with 32 bit of Windows. I plan to use the "Bash On Linux" on windows. It first came on 64 bits. I do not know if 32 bit supports it.
I prefer Chrome (and have usually 20+ tabs open) and not Firefox (which uses significantly less RAM).
My primary usage comprises programming (on light editors mostly) and lots of tabs open in the browser.
CPU does support 64 bit. Celeron 2840: http://ark.intel.com/products/82103/Intel-Celeron-Processor-N2840-1M-Cache-up-to-2_58-GHz