Short answer: Ubuntu-64 will work.
Longer answer: "AMD64" applies to both AMD and Intel. (Intel tried an earlier 64-bit processor named Itanium, but it didn't catch on, so they adopted AMD's approach.)
Unix is a common ancestor of both Mac OS X and Linux. Mac OS X is not Linux -- they are cousins.
EDIT: Apparently you have one of the early Intel Macs, which had "Core Solo" and "Core Duo" -- not "Core 2 Solo" and "Core 2 Duo" -- processors. These are 32-bit processors. VirtualBox does allow 64-bit guests on hosts running a 32-bit OS, but still requires a 64-bit processor (with hardware virtualization support). So the short answer becomes: none.
This also means this Mac cannot run OS X Lion (a requirement of the current beta which seems likely to persist to release). To confuse things further, after "Core 2", Intel dropped the "2" and used "i"-something:
- Core Solo
- Core Duo
- Core 2 Solo
- Core 2 Duo
- Core i3
- Core i5
- Core i7
These are all "Intel Core". You have one of the first two. The processor is listed in About This Mac under the Apple menu.
EDIT TWO: Perhaps VirtualBox's CPU detection code incorrectly identifies the Sandy Bridge (2nd generation) i7. Also, the new MacBook Pros boot into a 64-bit kernel -- the older ones booted into a 32-bit kernel (even though they had 64-bit CPUs, and either way allows 64-bit apps). This caused other problems with VirtualBox 4.0.x which seem to be worked around by booting into the 32-bit kernel. You might try that.