How can I check if a program is running for the first time?

Hard to guess what is messy if you don't post or describe it. An obvious approach is to have a setting named "ExePath". If you get null or a string that doesn't match Assembly.GetEntryAssembly().Location then it got either just installed or moved.

Since your question appears to be concerned about each user that launches the application, then you should design a per-user solution.

Using Properties.Settings will actually work and be efficient as long as the setting in question is user-specific.

However, if this is not desired or appropriate for your application, you could also write a user-specific entry to the registry.

For example:

        const string REGISTRY_KEY = @"HKEY_CURRENT_USER\MyApplication";
        const string REGISTY_VALUE = "FirstRun";
        if (Convert.ToInt32(Microsoft.Win32.Registry.GetValue(REGISTRY_KEY, REGISTY_VALUE, 0)) == 0)
        {
            lblGreetings.Text = "Welcome New User";
            //Change the value since the program has run once now
            Microsoft.Win32.Registry.SetValue(REGISTRY_KEY, REGISTY_VALUE, 1, Microsoft.Win32.RegistryValueKind.DWord);
        }
        else
        {
            lblGreetings.Text = "Welcome Back User";
        }

Seems that your problem is actually that if you move executable to another location/folder on the same pc, it loses somehow the information about the fact that it was already run at least once.

Using UserSettings, on Properties.Settings.Default.FirstRun should resolve your problem.

Something like this, a pseudocode:

if(Properties.Settings.Default.FirstRun == true)
{ lblGreetings.Text = "Welcome New User";
  //Change the value since the program has run once now
  Properties.Settings.Default.FirstRun = false;
  Properties.Settings.Default.Save(); }
else
{ lblGreetings.Text = "Welcome Back User"; }

Look on this sample how to achieve that in more detailed way.