from the out set lets just say that wireless and simple dont really belong in the same sentence but with patience perseverence and a little help from your friends (here) you should be OK.
1) adaptor,NIC and network card are the same thing. this is the thing that you plug into your machine to enable it to communicate with a network. you will need wireless NICs for your PCs and Laptops (you may run into some serious problems with your wifes antique but I wont be the one to tell you that they will be insummountable)For the PC I would suggest using a PCI wireless NIC and in the laptops you should use PCMCIA cards.
2) Next you will need a router ,Which is a standalone box that acts as the bridge between the internet and your network. having a router will mean that you only have to have the computer you are using switched on (but considerable funds could be saved if this should be an issue, using the PC as a gatway will not slow anything down, the data transfer speeds of even broadband internet connections are very slow compared to local network traffic).
I would recommend that you take a look around Dabs, Simply or wherever you like to shop online (or out there in the real world (shudder)) and look for a Bundle deal .
Its kind of pointless getting into the details of setting things up right now until you have done you shopping Read The Manuals.