To the best of my knowledge, things haven't really changed much on this count since 2010, although exFAT is likely to be more reliable in Linux. I do want to specifically address this point from your question:
Ideally, this partition would also keep "/var" and "/home".
The /var and /home directories both contain files or directories that rely heavily on Unix-style filesystem features such as permissions and ownership. From time to time, people try to share these filesystems (especially /home) with Windows, and I don't know of anybody who's done so successfully, except of course by using Windows filesystem drivers to let Windows access these partitions. I'd like to specifically caution against using NTFS, FAT, or exFAT on partitions mounted at these locations.
Most people who share data between Windows and Linux create a shared-data partition that uses NTFS, FAT, or exFAT for this purpose. They then mount this partition in Linux, either relying on a distribution's auto-mounter (which typically puts it somewhere under /media) or creating an /etc/fstab entry to mount it somewhere convenient (/home/reeddog/windows, say). This is usually convenient enough -- although it's not sharing the whole /home partition, or even your whole home directory, it's easy enough to put your important shared files in a single subdirectory of your home directory. You can even create symbolic links from places like ~/Music to an appropriate location in the shared partition. The limited-to-nonexistent access to Unix-style ownership, permissions, and other filesystem features isn't likely to be a big problem when you mount a Windows partition as a subdirectory of your home directory like this. It's unclear to me why you'd want to share /var with Windows (to be sure, I can imagine reasons, but it's unclear why you want to do this), but something similar might work with a subdirectory of var, if it's something limited enough in scope -- but I'd advise against sharing the whole /var directory.
As I noted above, there are Windows drivers for some Linux filesystems, especially the ext?fs family. I haven't used any of these in years, though, so I can't comment on their current reliability or which particular driver(s) would work best.