The monitor is not necessary. Most computing appliances (for example a firewall or NAS) run "headless" without any human interaction.
If you are building the Ethernet-serial project as a learning experience, that's OK. However if you are doing it for the price, you can get a very cheap pre-built solution. See for example http://www.lantronix.com/devic.....e-servers/
I have used the Xport Direct myself and it is fantastic.