Am thinking of upgrading to a new laptop (64 bit) and would like to install Ubuntu 12.04 or newer. Are they compatible?
Yes, it is possible to install either the 32-bit and 64-bit versions of Ubuntu on a 64-bit computer. Ubuntu has been released with both options since the very beginning (e.g. warty warthog from november 2004).
The version with an i386 in the name is the 32-bit version and the one with amd64 is the one for 64-bit computers. Don't let the "i" or "amd" confuse you, it's the numbers that matter.