I would use a step by step strategy.
1) Make a local installation of WP using XAAMP or similarl
2) Get 1.5.1 version from wp repository
3) Import all and check all is fine
4) Do a backup of imported data
5) Get a more recent version like 2.0 or so
6) Update and check all is ok and do a backup
7) Repeat step 5 and 6 with 2.5 then 3.0 and then latest WP version
Probably moving from 1.5.1 to 3.2.1 directly will work flawlessy, but a 2 3 step upgrade would be better so any upgrade habve to update less data in the DB and there is no risk to timeout half the way. Doing it locally help you configuring large memory footprint for WP (256MB or so), long timeout time for PHP 15 mins or so.. assuring you can update large amount of datea at every step. DOing locally it’s easy and you can make backupd and update faster than online. ANd you will end with a backup of last versione of WP you can upload to your new host