IA32 is what 99% of all Intel-compatible PCs are. Every processor since the 386 (386, 486, Pentium, Pentium MMX, PPro, P2, P3, P4, K5, Cyrix, K6, K7/Athlon, Duron, Athlon XP/MP, etc., etc.) has been an IA32.
IA64 is Intel's 64-bit chips, what they call the Itanium. It's completely incompatible with current 32-bit machine code.
The AMD64 is AMD's 64-bit chips, the Sledgehammer and Clawhammer. They haven't been released yet (AFAIK), but they're in the works. AMD calls that architecture x86-64, and it can be backwards compatible to current 32-bit machine code (I think it just has two modes, but I could be wrong).
You want IA32.
The difference between Mandrake UP and enterprise is just the kernel configuration. One difference is that the enterprise kernel has highmem support, but that's not the only one. AFAIK, if you didn't specifically select a different kernel, you're using the UP one (UP is uniprocessor, too, so as long as you only have 1 CPU, that's right -- if you have 2, then you probably need the SMP one). In any case, NVchooser should tell you which file to download.