I've finally hit that point where I need to learn how to program to get anywhere further in Unity, but there's so much overwhelming information out there that as a beginner it's hard to look through it all and understand what's useful in the context of developing with Unity. I'd prefer to learn C++ since that seems to be the most widely used in the developement community. My question is, what did other people on here use to learn programming? and What would be the best way for me (as a beginner with a very low budget and not a ton of free time) to get started programming? Thanks!
As Cyclops mentioned, Unity doesn't use C++, it uses C#. Since you are new to programming C# would be a good jumping off point.
Personally, I started by picking up a book and programming on a TI99-4A way back in the day (external cassette backup...which never worked properly). There are a number of good books to teach-yourself programming basics. Here's a couple of listings off of Amazon (C++ and C#).
Some of these books will include a CD with a compiler, samples, and examples. If they don't, here's a free compiler: http://www.mono-project.com/CSharp_Compiler
Avoid "for dummies" programming books...I think they are too simple. Avoid what is called "visual-c++, visual-c#,..." those normally teach a person more so on programming a gui, not to be confused with scripting a gui as with Unity.
The things you will need to concentrate on are: creating functions, passing variables, and class structs. (and of course syntax)
One last thing to add, you mentioned that a lot of developers still use C++. Yes and No. From my experience they use C, C++, and C# and a lot of custom libaries. The regular Windows libaries can be really bloated.
Just my 2 cents...and my first posting on Unity.
Agreed with Cyclops' comment
C++ is not the best language to learn for unity. You can use c++ plugins with it, but they have to be compiled ahead of time, they can't really interact with unity directly, and you'd need Unity Pro.
C# on the other hand is a great language to learn for unity.
The best way to learn that would probably to look through the links of this other question:
http://answers.unity3d.com/questions/4897/how-can-i-start-learning-unity-fast-list-of-tutorials
I'd like to add my two cents: definitely commit to learning C#. C# is quickly becoming a standard and already is the standard on Microsoft platforms. (XNA, XBLA, and a lot of 360 games are programmed in C#).
I had tremendous success with the book Head First C#, which teaches in a more fun, visual way. I had previously had problems learning from books, but Head First really sucked me in and made me finally commit to learning.