You have so many options it is hard to say which is the best answer, since you have not provided any information about the old system.
Best advice is to keep the old system in place until you have new system. When ready (as a planned shutdown) then use something like the SystemRescueCD to create the new hard drive partitions and 'clone' the old system to the new system. Depending on the new partitioning this could be a 'one-to-one' "cloning" (partimage/gparted) or a bit more involved. If possible and reasonable placing the old hard drive in the new system or external enclosure for cloning is one way to start.
You may/will need to re-install a bootloader on the new system, which is not really that hard. Boot from the installation media, answer a few questions and read the on screen message about using chroot then do something like for example;
/sbin/grub-install --recheck /dev/hda
You might want to make sure the new system boots into runlevel 3 the first time if the video interface is different also.
Take the time and plan (and maybe test) this migration, read up on the tools available and practice using them.
I backup my systems completely to external hard drives every so often (about once every month or six weeks) using the SystemRescueCD, takes about 2-5 hours depending on the system.
http://www.sysresccd.org/Main_Page
Other options and solutions are available, hopefully others will 'chime in' with advice and suggestions.
