first i would try to run the mint-installer and see what he proposes to do. perhaps its a good option.
manually partitioning shouldnt give you much trouble neither.
swap you may use the allready existing one. if you need or dont need a seperate /home is up to you. installing it all under / is simpler. i would go for a seperate / and /home
if you decide to install grub from the mint-installation, you may simply copy the entries from the ubuntu /boot/grub/menu.lst into mints /boot/grub/menu.lst (with a bit of luck it will work out of box and you dont need to do anything)
if it doesnt work out of box its (more or less) easy to fix.
post at minimum the output of
so people might be more specific :-)