Also: since the dual boot computer I have now can't see the Linux drive when it's running Windows (since ext3 is incompatible), won't that also mean that other Windows computers on the network will be unable to see that drive as well (unless I get the specific software people are mentioning to enable that)?
Without samba windows PCs will not be able to "see" i.e. via network neighborhood any
resources on linux no matter if it is ext3 or FAT32.
To complicate the issue there are other methods to share files other then SMB/CIFS (samba) like FTP, SSH/SCP.
There are lots reasons why you do not want your main i.e. / partition to not be FAT32. As stated before FAT32 does not have permissions required by the linux OS. Some secondary reasons. Your limited to a 4GB maximum file size and a FAT32 partition is easily corrupted.