My opinion is that Redhat/CentOS or Ubuntu LTS (based on Debian, I know) are more likely to have the best performing drivers and the most tested and stable configurations, compared with other distros. Thus, I wouldn't stray from those for prod systems. Then again, I'm no Linux expert and I don't want to start a holly war about which distro is the best. Your choice.
I would care about using 64-bit to access more RAM only after the performance is satisfactory. Thus, I would test 32-bit first. Also, running 32-bit Apache + mod_perl on a 64-bit OS would give you at most 4 GB of RAM for Apache. That's way beyond enough as you shouldn't need more than 1-2 GB for this process.
Face it, your hardware is very old. I'm not one to not understand a lack of resources (believe me) but we're taking a single core CPU that was launched 8-9 years ago
I don't know if you have 2x CPUs but, even then, your CPU power is very very low if I got the CPU model correctly.