Apple Partition is for older G4/G5 Macs, if you have a Mac with Time Machine it should have an Intel processor, so you should use GUID partition table. However, both of them are Mac-only, Master Boot Record is the one that works with PC and Mac but does not work with Time Machine.
FAT32 will let you use the drives with the 2 systems, but it does not do automatic backups and has an individual file size limit of 4GBs. This means that ig you have a folder with hundreds of files that add over 4GBs then the folder can be copied just fine, but if you have a single file that is ver 4GB then FAT32 won’t take it. It is also slow, unstable and unreliable compared to HFS+ (Mac only) and NTFS (Windows only).
Also, 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 HFSExplorer (Free), which allows you to read (see and copy out) drives formatted for Mac (But not write, so you can’t add files) or you can install MacDrive (NOT free), which is a software able to allow full HFS+ integration (Read and write) 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.