Ok, let's get some stuff clarified: Memory is usually referred to as RAM which does not use/have any "space".Your hard drive is also your storage. Aside from storing data, it also contains the Mac OS, all apps, and is the thing that makes your computer run/work. It needs space to do its work and you should always have at least 10 - 15 GB of empty space at all times.
The easiest to eliminate are videos, movies, photos, etc - get an external hard drive and copy over all the space hogging files, then delete them from your internal drive.
It also appears that you back up your iOS devices to the computer - that is great, but it seems to be taking up about half of the used space on your hard drive, so you must have a lot of stuff on your devices. One way to change that would be to back up your iOS stuff to iCloud (purchase storage there), that would gain you some more breathing room.
So, right now, your first screenshot shows you only have 30+ GB available on your drive; I'd suggest eliminating at least 50 - 60 GB so you'd have a minimum of 80 -90 GB available.