Eventually there will be no more 32 bit systems or at least very few. M$ is already phasing out their support for 32 bit OS. There are a lot of advantages to using a 64 bit OS. Travis talked about one of the big benefits. Look at the difference this way. If you had 100 people you have to shuttle from the hotel to the convention center and you had a choice to use a car that will hold 6 or a van that will hold 12 which method will be the quickest. Another way to look at it is what can handle more traffic a 2 lane country road or an expressway.
A 32 bit OS can run on a 64 bit computer but a 64 bit OS can not run on a 32bit computer hence Kenny the error's you got when you first tried Mint.
Stan, Yes you can replace one Linux distro with another. You just need to remember what OS you have installed on what partition. This is so you don't accidentally over write windows. Which brings me to another point when installing 2 OS's. Windows has to be installed first! The reason is that Windows and M$ do not like to share so they do not have the option to install along side anything so the result will be that windows will wipe out any other install. Also Windows does not have a boot menu. So make sure you have windows installed first then install Linux and when Linux installed it will also install a Boot manager either Grub or LiLO, although I haven't seen LiLO used in a while. The Boot manager will allow you to decide which OS to boot into.
But if you are thinking about trying Linux I would suggest taking Travis' advice and use a USB drive to check out the different distro's and LInux in general. I suggested to Stan to use Unetbootin They have a windows version and all you have to do is plug your USB drive into the USB port and run UnetBootin. It has a drop down at the top that will allow you to select a distro and it will download it for you and install it on to the USB drive or you can down load the ISO image your self (gives you a better choice of options) and use the text box down towards the bottom to choose the ISO image to use. Then all you have to do is restart the computer, make sure the USB drive is first on the boot sequence in the BIOS. Once you have chosen the distro you like and want to install it there is usually an Icon on the desktop to install it to the HDD.