No, the modem is the thing that connects to the internet with your ISP (internet service provider), who ever that may be, mine is Time Warner.
I use mine much the same as you do but I also have many Macs and my main Mac is an iMac with dual screens.
Most peripherals can be accessed wirelessly such as printers, storage hard drives (much like the Time Machine), I have a USB hub connected to my Airport Extreme (a TC without an internal hard drive) that has three USB hard drives including my Time Machine drive.
Three scanners and 4 printers. All useable wireless for the most part.
I hate cables and use them as little as possible.
If you setup your home network using the diagram it can free you from almost all cables and give good access to your devices.
You are doing great and have a handle on what to do. I am here should you need help.
You are very welcome, thank you.
I am in no hurry so please take your time.