Based on personal experience with a dual-boot setup used for exactly the same purposes (just with Gentoo instead of Arch), you need 5 primary partitions:
- EFI System Partition (assumign you're using UEFI to boot, which you really should be for this as it's way easier to manage than a legacy multi-boot configuration). Needs to be formatted as FAT32, will be automatically created by Windows during install. You probably only need 128MB of space here unless you're having it double as a Linux boot partition (MS bootloader plus a basic GRUB install is currently about 64MB and not likely to grow all that much).
- Microsoft Reserved Partition. This is that weird ~100MB empty partition that the Windows installer creates for reasons usually unspecified. It's largely unused these days, but some stuff on Windows still chokes if it's not there.
- Widows C: drive. Needs to be NTFS formatted (Windows has long since dropped support for using anything but NTFS for the C drive, and ReFS isn't exactly ready for consumer usage). DO NOT MOUNT THIS VOLUME BY DEFAULT FROM LINUX, it will eventually bite you in the arse (though do set things up so you can mount it read-write from Linux if you need to). Assuming you configure Windows and whatever game launchers you use to put things on the shared partition, this only needs to be about 32GB plus however much space you need for data that will be stored here.
- Linux root partition. Needs to be a standard Linux filesystem (such as ext4, XFS, or BTRFS). Doesn't really matter which you choose, as you won't be able to access any of them reliably from Windows. Personally, I'd actually use BTRFS on top of LVM, but you would need a dedicated boot partition for Linux to pull that off (which should again be a standard Linux filesystem, since pretty much all the standard boot loaders have better support for them), and would require some more effort to sanely maintain. If you choose to use the shared data partition for your home directory, you can easily (and safely) make this as small as 16GB without issue.
- Shared data partition. Should be either NTFS or exFAT. If using NTFS, use NTFS-3G instead of the kernel driver and set up proper user mappings (check the NTFS-3G documentation about how to do this). If using exFAT, probably use the FUSE driver and not the Samsung driver (and hope that MS can pull their heads out of their arses and propose patches on LKML that will actually get merged in the near future). This should ideally be most of your disk space, especially if you configure both Windows and Linux to utilize it to the fullest.
Updated to address comments:
Installing games in Windows on exFAT may or may not hurt performance when compared to NTFS. Most of the performance differences only really matter when writing files, not reading them (so you'll see some differences during updates or installs, but not generally during game-play), and even then the software would have to be pretty pathologically bad to show significant issues.
As far as installing Linux software on the shared data partition, you probably can't if you're using exFAT or NTFS, unless you add another layer on top to give POSIX semantics (and even then, you probably just can't, at least not through the package manager). However, you shouldn't need to. Unlike Windows, Linux doesn't waste huge amounts of disk space with dozens of copies of essentially the same libraries, so it's fully possible to have a working install of Linux with a full desktop environment including a complete office suite and a complete development environment for multiple languages/frameworks in under 8GB of space provided you store your documents and development work-spaces in a separate partition.