Just make sure all your computers are in the same workgroup and you should be able to share folders that contain music and pics on any of them (right click the folders you want to share and set this on the relevant Properties tab). The external hard drive will be hosted on the PC it's connected to, but all others in your network should be able to access it if you wish.
Email to a client like Thunderbird (or any other) is best just dealt with on a single computer imo, otherwise you can get in a bit of a muddle with what is downloaded where and what is left on the server. But if your kids are sharing the files you want to share on their machines, then you should pretty much always have access to your main PC to get your email, I think - right?
You probably don't need to buy any additional hardware to do this, as long as the PC directly connected to your external hard drive is on when you want other computers to get at it.
EDIT Forgot to say "see you in a few weeks".
