As a Uni student still learning (currently web-development), i want to eventually learn to program web applications. I also would like to eventually (in the future), be able to implement Bitcoins code in whatever i work with. What programming language should i choose as my first to learn?
Bitcoin is primarily C++, but you can work with Bitcoin in any language you like.
If you want to learn how to make web applications, I would recommend PHP or Ruby.
Your best bet is to go for the language that looks most interesting to you, and get something working with it.
There are full (or partial) implementations of Bitcoin in
Python, and probably more languages that I don't know from the top of my head.
The main implementations have encompassing APIs to allow other software to interact with the client. Learn something that you enjoy learning, if you'll need another language later, you'll be able to adapt to it easily enough.
You should start reading the core here in https://github.com/bitcoin/bitcoin if you see the language details:
C++ 68.2% Python 15.2% C 10.0% M4 2.7% Makefile 1.4% HTML 0.7% Other 1.8%
For the first programming language I would recommend Python. It's easy to understand and a lot of Bitcoin libraries already exist.