The FXO allows you to interface to an analogue phone line.
The FXS allows you to use analogue phone handsets.
The ATA, which I think stands for Analogue Telephone Adapater, is basically an FXS. There are some models which have two FXS (allowing two different extensions) and there are some that also have an FXO built in.
There is a fair bit on info on Asterisk out there, I believe that the best quality solutions come from utilising dedicated digium cards with plug-in modules for FXO and FXS depending upon your needs.
But the short answer to the original question is yes you can use linuxMCE as an answering machine on an Anologue phone line. It integrates with Asterisk and that, with the right hardware, certainly allows you do do what you want (and a whole lot more).