Hi there, here are a few things to consider if you want any drive to work on the 2 systems:
*NTFS is the best format for Windows but it’s read-only on Macs;
*The best File System (format) for Macs is HFS+, but it will only work on Macs and nothing else;
*You can format a drive as FAT32, which would allow it to work on BOTH Windows and Mac, but it won’t do automatic backups, won’t take files larger than 4GB and will have a high risk of data corruption;
*You can format it as exFAT, but only works on Macs 10.6.5+ and PCs running Vista SP1 or later, but does not have any of the drawbacks as FAT32, so you can do automatic backups on both systems (Then again, it needs updated computers to use that configuration);
*You can have a drive as NTFS to allow to work on any PC and then install on your Mac a free app from the Apple website called NTFS-3G, which allows your Mac to fully use (read and write) to NTFS and also do automatic backups with no restrictions on both systems, but since it is done using the NTFS-3G software, this configuration will only work on YOUR Mac and the others will only read from the drive (But they won’t be able to add files).
*You can have the drive as HFS+ to allow you to use it on any Mac and then install on Windows a program called MacDrive, which is a software able to allow full HFS+ integration on a PC, meaning that it is the exact opposite to NTFS-3G. However the same rules apply, only PCs with this software will see drives formatted for Macs.
You can make the partitions on disk utility on the Mac (Go> utilities> disk utility), the partition for Time Machine needs to be HFS+ and it should be as big (Or small) as you want…
Best of luck!