Question: How do I transfer files and apps from old iMac to fairly new iMac❓

Use Time Machine on the old Mac to create a backup to an external drive. Then use Migration Assistant to move the data from that to your new Mac after you set it up. Or, better yet, use the TM backup to move your data to the new Mac at the time you set it up via the Setup Assistant.

Please see > Move your content to a new Mac - Apple Support

I understand your desire for instant gratification and thus a speedy solution to your issue. The initial TM backup of any Mac takes the longest time. Yes, even several hours or more, dependent upon the amount of data to b/u and the speed of the drive and connections method. Once the first backup is done, the subsequent updates to that backup usually only take minutes because TM backs up only files that have been changed or added. I'd set the initial backup to take place overnight and walk away.

The only adapter you may need for a USB connected external drive would be a USB-A to USB-C adapter (plug or cable) to allow access to the USB-C port and potential speed boost available on your new iMac.

Other transfer methods will require other cables and/or adapters ($$) and imho are less robust and reliable, wi-fi being the worst. Migration Assistant can use the Ethernet ports to connect the Macs, but I can't speak for the reliability of that.

With TM and an external drive you also then have the means to implement a backup strategy for your new iMac after you have it set up. Ask any veteran computer user (Mac or PC) and they will tell you that running without a backup is a 100% guarantee of data loss.

OWC/Macsales is a great resource for Mac drives and upgrades > https://eshop.macsales.com

Consider giving them a call for questions and assistance. They're good people; know their Mac stuff.

Miki,

Your new 21.5" will likely be a downgrade in performance over your 2009 if the Refurbished 21.5" iMac has a 5400 RPM HD. Please check the tech specs of the computer you purchased. If I am correct, I would recommend returning for a refund ASAP and buy a 2021 24" Refurbished iMac from Apple. Buy one with a minimum of 1 TB of storage and that will be a HUGE upgrade over the 2009 and the Refurbished 21.5" model. If you do not, you will likely be extremely dissapointed in your purchase.

Also, to migrate please follow the simple instructions in Setup Assistant and Migration Assistant. This is the most reliable, the easiest and overall the fastest method of migrating.

To get rid of the old one first thing to do is prepare it using the instructions in What to do before you sell, give away, or trade in your Mac. After you have done that you can recycle it if you want, please contact Apples's recycling program at Apple Recycling Programs and search for your country. If it is too old to have any trade in value then Apple will responsibly recycle the computer.

Understood, good luck!