Our new desktop is being delivered today. Should I do all updates on the computer before setting up the new one ?

It sounds like you also have an older Mac and you are asking if you should update it first. Can you confirm that is what you want as your post is not clear. If you do have an old Mac, please let us know the version of Mac OS installed on it.

OIf you have an older Mac and want to migrate it's information to the new Mac, yes the old Mac should be as up-to-date as possible not Mac OS but the applications it has installed. The new Mac will only run 64 bit applications and your old Mac may have some legacy 32 bit apps, if it does those need to be updated or replaced in order to migrate your apps. On the old Mac open System Information - Software - Applications and you will find a list of apps that are 32 bit, just pay attention to your 3rd party apps!!!!

Finally, if you are migrating from the old Mac to the new Mac please follow the directions below:

When you buy a new Mac the easiest, quickest and most reliable method is to simply connect the old Mac's Time Machine External Hard Disk to the new Mac using a USB cable before you turn on the new Mac. When you start the new Mac for the first time it will startup Setup Assistant (SA), SA will get to a point where it asks if you are migrating from another computer, select Yes  and follow the on-screen prompts and it's done! It is THAT simple. NEVER EVER use Wi-Fi, Ethernet or USB from the old Mac to the New Mac, use the method stated. 

If you have already done SA on the new computer then simply connect the Time Machine External Hard Disk using a USB cable and launch Migration Assistant (MA) which is located in Applications - Utilities - MA. Then follow the on-screen prompts.

The ONLY difference between MA and SA is MA will create a new user account that you need to log into.

Both SA and MA migrate applications (not 32 bit apps) , data files, settings, it does not migrate Mac OS itself. Some professional apps such as Adobe and Microsoft apps may require re-installing their apps as they will not allow them to be migrated. As long as you kept the security keys for installing their apps, it is not a big deal.

I wouldn't. When you first turn on the new iMac select to use Migration Assistant to move your files from your old computer or Time Machine backup drive to your new Mac. That will create your original user account on the new Mac.

If you first boot up without migrating you'll end up with two user accounts, the one you created and the one from your old Mac. It's a pain to straighten out.