I will be using an Ubuntu VM in Mac OS X with VMWare Fusion but I'm not sure which version will give me better performance (32 or 64 bits).
I believe the 32 bits version should take up less memory, but I'm not sure. What do you recommend?
Unless you plan on giving the VM more than 4 gigs of memory, there's no need to use the 64-bit version. A 64-bit operating system can address more memory than a 32-bit operating system, but if you have less than 4 gigs available, then it doesn't matter, since a 32-bit OS can address that much. They should both give you equal performance, but some software is not available for 64-bit linux and is for 32-bit linux, so you would probably be better off with the 32-bit version.
The memory is whatever you provide the VM with, bitness has very little to do with it here (except that the 32-bit is limited to a maximum of 4 gigs).
The real issue will be speed of commands and virtualization, which is where 64-bit will give you an advantage. Using the highest bitness available on your processor for the process will not only give the flexibility to run 64-bit Ubuntu, it'll also allow you to run that using hardware virtualization instructions. I'm not sure if the 32-bit version takes advantage of them (I know it doesn't require them, though).
The performance difference won't be huge except on large operations or large memory, but in general, if you would buy 64-bit hardware (what VMWare is the equivalent of here), you should use a 64-bit app.