Upgrade advice / starting again

ive been using zencart since 1.3.7a and upgraded through all the upgrades,

problem i now have is that the database is large and prob full of old plugins and data from none compatible items etc etc etc

what im looking / wanting to do is start a fresh install on 1.5.1 install all the mods i want and work, then create a new template etc etc etc, then import all my items, customers, orders etc so i have a nice new clean website.

is there an easy way to import the data i need, and can anyone think of anything else i need to import??

I think a better solution would be to follow the steps recommended by DrByte with a small extra step. Just before you bring in the old database, compare the two for tables that do NOT exist in the newer database. Those (if any) would more than likely be leftovers from earlier mods.
For example, the Scheduled Events mod adds and eventz table to the database. If you are no longer using it, just delete the table(s) from the old database prior to step c).
Another give away is a table that does not have the same prefix as that of the whole database IF your database has a prefix.
Trying to pick and choose what to bring over from an old database is just too risky.

thanks ill read through that