Go 64bit - generally speaking, 32bit Linux is dying off as 64bit has been out for a really long time - some distributions have stopped making 32bit altogether these days (RHEL/CentOS 7, Arch, etc.). If that CPU is 64bit capable, go that route. If you step back and think a little meta, the kernel coders focus on 64bit so your upstream brain trust is all involved, whereas in 2018 the 32bit side of code plays second fiddle. Unlike the Windows side which I know is still struggling to get everything to 64bit, in Linux it's been baked in and working for probably a decade.

A 64bit base OS can run 32bit applications (with the appropriate extra software installed - you have to add 32bit glibc + friends to the 64bit OS for it to function), but a 32bit OS cannot run 64bit apps - the "word size" (Linux kernel computation unit, in this case - not the natural CPU boundry){1) will not allow for a 64bit application to load into a 32bit kernel, but the larger can accept the smaller. I'm pretty sure you'd take a performance hit running 32bit apps on a 64bit kernel, but I've never profiled it to know for sure.

Even 32bit ARM (small embedded devices, like the Raspberry Pi) are starting to die off, 64bit ARM is becoming the standard for that market as well these days.(2)

(1) https://en.wikipedia.org/wiki/Word_(computer_architecture)
(2) https://en.wikipedia.org/wiki/ARM_architecture#64/32-bit_architecture