Securing a connection to the internet

I am in the process of making a Server and a Client application that will communicate with each other, probably through RF or infrared electronics. The idea is that the server downloads a zip file from a certain IP address, at which a web server resides which sends the zip file back to the server. The server then unzips the file and uploads one of the files inside to the client.

Now my problem is that I want to make the connections as secure as possible. I want to make it so that the web server only accepts connections from my servers only and no other programs, and that goes for the server and client as well. I also would like to make it so that the connection can't be intercepted, thus ensuring that bad or false data isn't being sent by someone to hack either program. And finally, I would like to be able to ensure that the whole file is downloaded, even if the download is interrupted somehow. If that's the case, I want to restart the download, but it doesn't matter if it's from the beginning or if it resumes the download.

I'm not asking for someone to write the code here, I'm merely asking for some ideas on how to do these things that I can't seem to wrap my own head around, so that I will be able to implement this in Java.