dual boot - Which Ubuntu should I run on my Windows PC

I intend to dual boot Ubuntu 16.04 and Windows 10 but I'm a bit confused about the information on the official Ubuntu website:

64-bit PC (AMD64) desktop imageChoose this to take full advantage of computers based on the AMD64 or EM64T architecture (e.g., Athlon64, Opteron, EM64T Xeon, Core 2). If you have a non-64-bit processor made by AMD, or if you need full support for 32-bit code, use the i386 images instead.32-bit PC (i386) desktop imageFor almost all PCs. This includes most machines with Intel/AMD/etc type processors and almost all computers that run Microsoft Windows, as well as newer Apple Macintosh systems based on Intel processors. Choose this if you are at all unsure.

Now, my Windows machine is 64-bit with Intel processor. Which of the architecture of Ubuntu should I install, 32-bit or 64-bit

For sure is better to go with 64bit version. Today (22th Apr 2016) I would still choose Ubuntu 14.04 LTS and not the 16.04 LTS version. The 16.04 was released just yesterday and there will be a lot of bugs still to repair. (this is just my personal opinion...)