How do I connect my old router to a new iMac?

See this article for assistance: Transfer to a new Mac with Migration Assistant - Apple Support

Don't worry about your iTunes music, the iTunes library will migrate along with everything else. When you open the Music app the first time, it will import your iTunes library. If you follow the directions per the video, your new Mac will look virtually the same as the old one except any old 32bit apps will not come over and there is a possibility professional apps such as Office for Mac or professional Adobe apps may need to be re-installed.

I have used Setup Assistant/Migration Assistant for many Mac migrations and have NEVER had a problem with it.

Here is an Apple YouTube video that explains how to:

https://www.youtube.com/watch?v=24IgIZrGYkw&t=27s

Although they are all discontinued, the more recent AirPort Express models (including yours) remain fully supported and will work fine. If it's working, leave well enough alone.

Is your router not working? Is it an Airport Express or AirPort Extreme. Is your iMac connected to it via Ethernet cable or WiFi. If it's close enough to the iMac Ethernet is best and fastest.

If it's working OK you don't need to replace it.

Your AirPort Express should work okay however remember by today's standards it is quite old and you may have new needs that you haven't thought much about. Things like, gee it should be nice to Bec able to sit on the patio in the back yard and use my iPad to get e-mail, work on a project online, surf the net etc...

As long as it's working OK keep using it. When you upgrade to a newer router be sure to check the compatibility with your modem. I tried a Nighthawk mesh system and it was not compatible with my Frontier modem. Couldn't get an internet signet from the modem to the router with the ethernet cable. Don't know if it was the modem or router that was the culprit. I decided to go with my AirPort Extreme and an extender rather than a mesh system.

I still buy Apple airports cos they are great for my needs. The ones with Airplay are great for playing music all over the house. The Time Capsules are useful and easily upgradable with bigger disks It's so easy to add one to an existing Airport network either to extend coverage or add, say, an ethernet point. I love them and I've got a drawer-full of them for when the ones I'm using give up the ghost. I can't imagine why you'd want to bin them. They'll work fine with your new Mac.