For the backup drive? No reason at all - Linux will read and write to NTFS filesystems. However for the OS system itself, you should be using ext3 or one of the other Linux filesystems that were discussed earlier.
But for starters - you should find ext3 fine - its a good all round filesystem. However you can always add partitions with other file systems if you feel the need. You can have a partition with NTFS on as well. (As an example - my dual boot laptop has3 NTFS partitions for Windows, and 3 ext3 partitions for Linux. The NTFS partitions are mounted under the linux system so I can access those files when the system is booted to Linux - which is 90% of the time!