Hi Mario,
LuaSocket is more versatile, so that's a good choice. I'm interested in its possibilities. Currently I only use it for determining a client's IP address/hostname and for sending e-mails from within the application, which works great. The main program stores data to send in a mail-queue table in an SQLite3 database, another running Lua program (the mailer) checks the mail-queue every X minutes and sends the e-mail. If it fails, it tries again later. I chose to use a separate mailer program, because sending e-mail blocks. I measured 3 seconds for sending an e-mail successfully which is too much for a game. If it fails it may take even longer.
You could mention Copas and point readers to their website. They have good documentation and examples your readers can explore themselves.
You're right about SQLite3, I think it would take a large amount of pages to inform readers about it.