Your LAN (Local Area Network) speed is independent of your internet connection speed. The internet speed is regulated by your ISP the LAN speed is specified by the IEEE 802.11 standards and dependent on the hardware built into your internet devices. In this case your Mac Pro will most be the limiting factor at 802.11g or 802.11n but in either case the speed is the same in both directions.
  1. On your Mac Pro while you still have a monitor and keyboard attached
    1. In System Preferences > Sharing
      1. ✔ File services - choose which drives and folders you want your iMac to be able to access then specify which users will have access to each and whether they will have Read only, Write only, or Read/Write. Choose a user account on the Mac Pro and grant them Read/Write access.
      2. ✔ Remote Login — Allow access for the same user you chose in File Services
      3. ✔ Remote Management — Choose the same user you chose in File Services then click options and check every option available.
    2. System Preferences > Users & Groups > Login Options > Automatic Login — specify the user named in File Sharing
    3. NOTE: It is essential that you choose the same user in each case or this will not work correctly! Don't ask how I know that to be true. blush
    4. Verify your Mac Pro is logged onto your Local Area Network
    5. Do NOT remove the monitor and keyboard from the Mac Pro until you know everything is working correctly.
  2. On your iMac
    1. Assuming your are logged onto the same WiFi network as your Mac Pro, in the Finder sidebar under Locations you should see your Mac Pro. If not check the settings on your Mac Pro.
    2. click the Mac Pro icon and you will be presented with options to Connect or Share Screen. — in either case you will be prompted to log in. Use the same user account name and its password that you specified in setting up File Services, etc. Note: You can save the userid and password in Keychain so that will be automatic in the future.
    3. For a superior screen sharing experience install Screens 4 on your iMac and use it instead of Finder to share the Mac Pro's screen.
    4. Once you are satisfied everything is working correctly you can shut down the Mac Pro, remove its monitor and keyboard, reboot the Mac Pro and thereafter logon from you iMac via Screen Sharing.

FULL DISCLOSURE I have no relationship, pecuniary or otherwise with Screens 4 or their publisher other than that of being a satisfied customer.

If we knew what it was we were doing, it wouldn't be called research, would it?

— Albert Einstein