A few thoughts:
FAT32 isn't a very good file system (as mix says) but because it's so old, pretty much anything can read it (software to back/restore up the vulnerable partition tables can be had for free and and helps a bit). NTFS is a bit better, it just has different failure modes. HFS+ (Apple) is OK, but is getting a bit long in the tooth and just has different failure modes. Same for Ext3, and Ext4 is still not as stable as it should be.
NONE of them prevent bit-rot or ensure data integrity.
I dunno about Paragon NTFS for Mac, but Paragon HFS+ and Paragon ExtFS for Windows work pretty seamlessly - I use Tuxera NTFS Pro to read NTFS for Macs - it is quick and has never given me any trouble.
Yes, there are lots of good apps for resizing HDDs and setting up different filesystems in freed-up parts of the drive - I like EaseUS Partition Master but there are other good (and bad) alternatives. Personally I prefer to have only one filesystem on a single physical drive - it just makes things easier
I really wouldn't buy the sort of huge drive that mix suggests. Yes, it is convenient in a way, but it is a single point of failure and nobody really needs that. Most of the SOHO OSes have problems with drives over 3TB anyway.
Your best and safest and simplest bet is to get a couple of Western Digital Blacks and put 'em in USB3 enclosures (I like NexStar) and use 'em for your backups - one for Windows and one for the Mac.
You wanna be clever, get a big drive as mix suggests, split it into a Windows and and Mac partition and backup your backups to that.
You wanna be cleverer, buy ANOTHER couple of 3TB WD Blacks and another couple of good enclosures and use then to alternate your backups. OSX/Mac is smart, you can tell it to use 2 drives for Time Machine - it'll use number one drive for the first Time Machine image, the number two drive for the 2nd Time Machine image and then back to the number one drive for the next Time Machine image and then the second drive for the third image and so on. You can do the same with Windows but it requires a bit of minor farting around with scripts and cron (I mean PowerShell and Task Scheduler).
And keep spare copies off-site in a secure environment (I use the father/ grandfather/son system)
Finally, consider dropping off most of your local physical junk and using iCloud to backup your Mac and OneDrive to backup your Windows (you DO have all your essential passwords written down twice somewhere findable don't you?) And there are other good services. That's the place we'll all be in a few years in countries with fast cheap broadband connection speeds.
[In my country (South Africa) affordable broadband is horribly slow and the national electricity grid is collapsing, so those who can afford it are falling back onto big batteries/inverters, solar and home generators. I don't know how much longer we'll have our (slow) ADSL before we fall back to POTS and cell-data and eventually (only for the very wealthy elite) satellite only (and it won't be fast)].
Think carefully and you can save yourself some bucks.
And ask yourself just how much your data is worth.
Mac
[now I'll wait for mix to tell me that I have the brains of a mouse, the intelligence of an earthworm and shouldn't even be permitted to ride a tricycle
]
FINALLY, a backup of any kind (particularly a system backup) is not a backup UNTIL it has been tested for REAL to reliably restore onto bare metal from a startup CD and your system drivers.
Yes, I know it's a major drag to test but until you have shown it CAN be done successfully then your backup is likely to be just a reassuring delusion.
