128gb is not a lot in the modern era.
When you install Linux you will have the options to put different parts of the system on different drives. The root system / contains everything. Within that is /home which contains all user owned files; that's where your desktop, your files, media, games etc are kept. Outside the home folder all the other folders in / are system folders. But you can have different folders in the Linux system be on different hard drives and partitions - they don't have to all be together as one simple file system .
Any folder can be on any drive (mounted on any drive) as long as Linux is told where to find things. It's very common to put the /home folder in its own partition - either on the same physical drive as the main is but in its own partition or it's own entirely separate physical drive. That keeps all your personal files and folders separate from the OS, so you can easily change the OS and preserve your personal stuff for example.
So in your case you could do this:
- SSD --> / (linux OS partition)
- HDD --> /home
The upside is the OS will load faster on the SSD, and your Home folder with have plenty of space for the future (which will be by far your biggest, as you fill it with games and media). The downside is that games (Steam, GOG etc) will install into /home so will not benefit from the SSD.
The Linux partition / only needs to be about 50gb, so you could make space for games. But check the requirements and recommendations of the Linux distro you're interested in as its annoying if you run out of space for the OS and would need fixing later. You may need a bit more than 50gb if you're a heavy user of things like flatpak at the system level for example. The rest of the space on the SSD could be for games:
- SSD - 50gb --> / (linux OS partition)
- SSD - 78gb --> Games partition (/mnt/games)
- HhD - /home partition
The Games partition here would be seen as a separate drive (so would be mounted in Linux somewhere like /mnt/games) for example. This would behave like a Drive D on Windows, appearing in your linux file manager as another drive in the same way a USB or CD drive appear. It can be set up to auto mount when you load Linux so it's always there.
Or you could mount the space on the SSD as if it is a folder under your home partition - so for example:
- SSD - 50gb --> / (linux OS partition)
- SSD - 78gb --> /home/username/games partition
- HhD - /home partition
This should work - so most of /home is on one drive but one subfolder is on another. It'd look like it was just another folder in your home folder. BUT it could get messy - for example if you ever fiddle with it in the future you could break something. You could even forget you'd done this and break something if you decide to reinstall etc. I'd personally just mount the game partition as it's own drive so it's clear what it is.
In either scenario a GOG installer will see the location as a drive or folder and install directly in there if you point it there. If you use Lutris it's easy to have all your gog games install to one place.
Steam usually installs games into a hidden folder in your home folder (E.g. /home/username/.steam) but you can easily add the drive as an extra library location in Linux in exactly the same way as you can have multiple locations in Windows. Then when you install games you can have the home folder still be the default but specify your Games SSD partition for your flavour of the month big game you want loading fast.
Having said all that the another option to seriously consider is replace the 128gb drive with something new and decent like a 1-2tb SSD. If you have a 128gb drive I'm guessing it's a few years old so it may pay to future proof your device with a new drive. Moving OS is a good time to look at the hardware as it's worth doing that just before you install the new OS.
In that situation you could partition the new SSD as follows:
- SSD - 50gb (or more)--> / (linux OS partition)
- SSD - 1950gb --> /home/ partition
- HhD - 2TB --> whatever you want
Then all your files would be on the SSD including all games, so they'd all benefit from the higher speed. The other HDD could be used for anything you like - more files space or backup space or store all your media files that really don't need to be on the SSD.
Overall, if I were in your situation I'd get a new drive if I could afford one for the best overall experience. If I couldn't I'd put the OS and a games partition on the SSD and the main home folder on the HDD. This way you could also easily still get a new bigger ssd in the future and migrate your home stuff over to it later on from the HDD.