|So I have to find a switch big enough for me to connect all the equipment to or is there a workaround for that?|
No. First you have to ascertain whether or not the printers in question are "network printers" Which is to say, do they have a network interface on them with which to connect to the network?
If they don't, you'll have to look at getting a "print server" type device that does. The type you'll want will connect to the printer(s) via a USB cable. HP makes a device like this called a HP Jetdirect external USB print server You might need to google that to get an idea what you'll be looking for.
Then once all your printers are network capable, then you can follow paulsep's advice about a switch.
NOTE: I'd use a switch before I'd use another router to add more LAN ports to your network.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.