Should I use mod_php or PHP-FPM for WordPress on Apache2?

If you could provide the exact error you see it could help us find what's going on.

How much traffic do you expect for this site? How many servers/infrastructure setup do you plan on using?

My first thought, unless you can take advantage of the features PHP-FPM will give you, you should stick with modPHP since it's easier.

I prefer mpm-itk :)

That's what I use, also, with mod_php. With both, I can completely isolate user accounts and virtual hosts from each other, which provides more security than other methods, in my opinion. My setup prevents one user from even reading the home directory to list other possible user accounts, so they couldn't get into others folders. It seems fast enough, and only uses about the same memory as the prefork mpm.

I'll second mpm-itk as well.