I have an SSD and a HDD in my computer. The SSD is divided into two partitions, one is Windows and the other is empty. It is less than 60GB. I want to install the Linux system itself on it, and move all personal data, programs and all other data not related to the system to a separate partition in the HDD. Is that likely? If so, how?
Yes, that is perfectly possible. You can install the Manjaro root filesystem on the SSD, and then create a partition on the HDD for
/home. The latter is where all your personal data will be stored.
Do however bear in mind that
/home must be a Linux-native filesystem. NTFS or any of the FAT variants are not supported, because they cannot store POSIX file ownership information and POSIX permissions. If you want to be able to exchange files between GNU/Linux and Microsoft Windows, then you should create an additional partition with an NTFS or FAT32 filesystem on it.
More information ─ albeit post-install ─ can be found in the following post.
Do you have a computer with UEFI Bios ?