Answers to the questions I think are in there:
Yes, you can wirelessly print to a 4420 with a wireless card, as long as the home has wireless.
The router does not act as a server, it acts as a router. It will take the print job from the PC and "route" it to the printer, as long as you configure them both to be on the same network/IP scheme and print to that IP.
Do you need a wireless print server? Well, the answer to that is "no" if you have a wireless card in the 4420 and "yes" if you not.
The $100 for the wireless print server is usually cheaper than the wireless card in the machine.
Paragraphs... use them.