How should I ship an iMac desktop? Who should I use, UPS? FedEx?

For the best insurance coverage against damage, take it to the carrier storefront with the original Apple packing, have them pack it, and insure it.

I’ve used both UPS and FedEx for larger packages and shipping around computer servers.

Who you choose as your carrier is entirely up to you.

About the contents of the Mac...

What to do before you sell, give away, or trade in your Mac - Apple Support

Or if you’re planning on using the Mac and its contents in Morocco or in Massachusetts, after the Mac arrives from Canada or California, have backups of your data. This on the off chance something happens en-route.

If you have sensitive data on the Mac and wish to preserve it, encrypt it.

I recently purchased a 2 new iMac's from Apple and the shipper was UPS, both arrive in fine condition. Please make sure you spend the money on adequate insurance and don't be afraid to over package. Personally I don' t think there is a "best" anything. There are options for almost every product and you have to decide what is best for your needs. I'm telling you UPS did fine on mine and the next person may say the exact opposite, the same holds true or FedEx & DHL.

Either should be just fine in terms of having it arrive safely.

More likely, the decision should be based on the delivery

options available at the destination and cost.