How big to make partitions is a difficult thing to answer, only you will really know the answer when you either get it right or realise you got it wrong and what you probably should have done!
For me I'm a heavy web user and Firefox eats memory, my system only has 16GB and I can't add more so I opted for a 32GB swap partition. If you have loads of RAM and you never really find yourself using it all up maybe a couple of gigs would be enough.
My root partition is 64GB and is almost half full even though I don't have all that much installed on my system. The version of Mint I'm on uses Flatpaks for a bunch of things and they are way bloated compared to system packages. Maybe it's a good thing to have browsers in segregated containers, other things not so much.
My home directory is 100GB-ish and only has about 30GB of stuff on it, but it's not really intended for mass storage of music and photos and so on, my main storage unit is my NAS. Ideally I'd have my system periodically backup my home directory to my NAS so I could wipe my drive and start over if I really wanted and not loose a thing, but as it stands I'd loose my browser sessions and emails since I last did a backup. All my really important stuff is on my NAS.
One thing to consider is that is possible to resize partitions (at the end of the partition) without loosing data, but as far as I know it is not possible to change the starting position of a partition without at least potentially loosing your data on that partition. I think this is the reason why /home is usually near the start of the drive.
So you might have something like -
Boot - /boot/efi - 512MiB
Home - /home - ??GiB
System - / - ??GB
Swap - no mount point - 2GiB (or 32GiB if you're like me)