Hi jonnmso and welcome to bytes.com!
If you're interested in web applications, some recommendations would be JavaScript, PHP and Java. I would also recommend learning about XML, bash and
unix-like OSes (e.g. Linux) in general as these are commonly used in combination with webapps.
Concerning mobile apps, those are normally written in Java (Android), Objective-C (iOS), C# (WP8) or HTML5 and JavaScript.
In any case you should learn about networking protocols (e.g.
IP,
TCP,
UDP,
DNS,
HTTP,
SSH,
TLS/SSL,
BitTorrent, ...) as these are the backbone to any data transport you'll be using.