It depends. 64 bit Windows is obviously more powerful and run faster on goof hardware. But if you have poor Mac hardware you would probably want to install 32 bit version to keep it lighter.
I've using a trial version of Parallels Desktop right now and when I was installing Windows 7 there were no option to choose 32 bit or 64 bit. Correct me if I'm wrong but I understand there should be a checkbox if I want to install the 64bit version. Is this because I'm using a trial version?
The option to install 32 or 64 bit isn't a Parallels option, it's a Windows installation option, depending on the installation media you either have a different downloads for 32 or 64 bit, or, if it's a DVD, I'm told both version come in the same DVD and you have the option to pick whcih you want to install.
Right, it means there is nothing in Parallels Desktop settings need to be checked in order to specify your Windows bit version.