Move or Install Apps on HDD not SSD

You don't have to do that!

As you have read elsewhere the best answer is, don't mess with the system folders. You can move the /home folder to a dedicated partition in the HDD (your sdb) using the official help page However, I recommend keeping the /home as well as /home/[upir user ID] in the SSD as all your personal configuration files are there. Keeping the personal configuration in the SSD keeps the system snappy.

Steam

Steam games take up a lot of space. However, it does not keep the games in the system folders, such as /usr. Your steam games are in /home/[your user name]/.local/share/Steam. See Where are Steam games installed?

See Installing programs in root vs home partitions? for more on the how to use an SSD and HDD.

Follow the instructions in Do I need Intel Smart Response when installing Ubuntu? to move some of your large personal folders like ~/.local/share/Steam to your hard drive and create symbolic links to the SSD.

I recommend creating an ext4 partition in sdb so that file and folder permissions used by Ubuntu can be preserved. These will be lost if you dump the folders in a NTFS partition. See I want to reformat my home partition from ext3 to ntfs

Also see How to save applications for re-install or upgrade? for why moving some apps to a different partition and keeping the default apps in their original place is a bad idea.

Hope this helps