Yes and no.
If you are new to using Ubuntu I would suggest that you use the guided installation and install all of Ubuntu to your SSD. Your system will benefit from /home on the SSD because that is where a great deal of software will save configuration files. Putting /home on a HDD will slow the launch of any software that stores files there.
The file system hierarchy in Linux is not similar to Windows. You can't really install software wherever you like. The exceptions would be software you compile yourself, and luckily for your situation, games on Steam and similar platforms. Most games that are compatible with Linux you will be getting from Steam and Steam lets you create a data folder for your games wherever you like.
For other software, like all of the software you get from Ubuntu repositories, you can't choose where it is installed. There are ways to finagle the file system to install software files in other places but this is not something that's very easy to do, and can quickly become problematic, especially if you are not familiar with solving problems in Linux. The majority of software in Ubuntu repositories don't take up a lot of space. Compared to games which can take up several GB, most Linux software is miniscule in comparison
It's also not so easy to delineate between "software" and the operating system. Ubuntu is a collection of lots of software. If you wanted to install all your "software" to the HDD, how would you make sure that doesn't include your file manager, web browser, text editor, image viewer, etc? Presumably, these are all applications that you want to launch quickly, so storing all your software on a HDD pretty much defeats the point of putting your root file system on a SSD for speedier load times.
You are also not restricted to saving personal files on /home either. You can put your movies, music, documents, pictures, and other files wherever you want.
The guided installation is generally the best option for most users, especially people new to Ubuntu. If you put your Steam folder on the HDD and store your files on the HDD instead of /home, you are going to find it very difficult for your OS to max out 128 GB, even with the configs stored in /home and the Ubuntu software being located there.
