No advantage to 32-bit anymore. In the old days there weren't as many
packages for 64-bit and flash was a problem for some people. That has not
been the case for about five years. I have run 64-bit since it came out.
The advantage is mostly in the way the chip works. It is faster. It
addresses more RAM, etc. You might encounter the odd application that is
32-bit only, but now Ubuntu can install 32-bit applications in a
64-bit installation. The only problem that I could foresee is if you have a
special circumstance such as a graphics card which is not supported by the
kernel and you have to go outside the repositories to find one. It may only
come in 32-bit, but that is a long shot.

If I understand you correctly, I can choose to install either the 32 or
64 on my laptop and either will work well on the machine.

The 64 bit download says amd64. I may have had the wrong understanding.
I assumed that this could not be used on the intel chip. Please correct
me if I am in error.

Yes either will work fine. What you get with 64bit is access to more
memory ( assuming you have a system that can take oodles of it and you
want to stuff as much in as you can ) plus it allows use of special
64bit routines in the CPU which the 32bit OS has a long-winded work
around to use.

I was unable to use 64bit as the Dell colour laser driver ( actually a
re-badged Xerox Phaser 6000 ) is 32bit only and try as I could it
would not play ball with Kubuntu 64bit. Not too disheartened as the
printer is excellent and using an SSD for the OS means it's pretty
fast anyway so any performance boost would be moot :-)