How to determine what iMac I have

Hello, does it bot into Restore Mode?

One of these?

Command (⌘)-R

Install the latest macOS that was installed on your Mac.

Option-⌘-R

Upgrade to the latest macOS compatible with your Mac.

Shift-Option-⌘-R

Install the macOS that came with your Mac, or the closest version still available.

If so, look for Utilities menu at top of display, open Terminal & type...

1. Type or paste this command in Terminal: system_profiler SPHardwareDataType
2. Press Return to enter the command. Terminal then shows a hardware overview that includes the model name and serial number.

Terminal is also available from the Utilities menu when you start up your Mac from macOS Recovery.

Also, many if not most iMacs have the Serial# on the bottom of the stand...

Check Your Service and Support Coverage - Apple Support

I figure that I should try to sell it, but I cant find any identifying info on the exterior.

iMacs have been in continuous production since 1998 so you've given us quite a massive field to search.

We can narrow the model a bit. The iMacs this forum section covers were all made before 2006. Is yours that old?

For hardware the purchase history is associated with your Apple ID, not the history that tracks app and music purchases.

The problem you'll have if you did not save a paper or electronic copy locally (your file cabinet or computer) is you may be out of luck. Apple leaves a copy of the invoice link to the device in your Apple ID list of devices if you bought directly from them, but the link disappears after about 18 months.

Check your Apple ID device list to find where you're signed in - Apple Support

Scroll that page to the section labeled, "Use the web to find where you're signed in."

If you bought from an Apple Authorized Reseller or a third-party reseller, only they can hep you find an invoice or receipt.

Re BDAqua's excellent advice, "footed" iMacs with the serial number on the bottom of the foot started in 2004 so yours should fall into that class. This is what Apple shows for the sticker location on the "foot."