Can I use any of this stuff to get access to printers from other rooms without having to go through other computers? Or do I need to head over to Wal-Mart and buy some sort of Netgear something-or-other?
Kind-of need to know make and model of these printers, so we can look them up. Some very inexpensive printers don't like to be anything but directly cabled from the computer you're printing from.
Here's how I would do it, if you're printers support it. Any printer these days that costs over (Oh, I think) $125 or so, already has an ethernet interface. Cable them directly to your switch. If they don't have an ethernet port, get a print server with a USB interface. They're not expensive. (But first, check to see that the printer can be run this way). If the printer has neither ethernet nor usb, dispose of it. It's ancient.
Set your network addresses on the printers static, and outside your DHCP range. On each computer, set up the printers to print to that IP address.
My way, done right, is rock solid reliable.
Wireless printing, the way I usually see it done, isn't (IMHO, YMMV) as reliable.