I'm looking for something to help me calculate cointegration/correlation, evaluate trading strategies, and generate trade signals.
There's not a whole lot to learn. Excel can calculate correlation between sets of data fairly easily without having to know the specifics of the calculation.
Yes R can help, although it's mostly a statistics platform and is structured as such. The language itself is a bit clunky, but there's tons of nice packages.
R is an outstanding programming language that will enable you to test any kind of strategy you can dream up. It is free, well documented and well supported. Highly recommended by this humble trader.
Just about any program can test just about any strategy you can dream up. You can do just about anything in excel. The difficulty comes from being able to describe what it is you want to do, and having the knowledge to implement it. To OP. If you want a tool with the functions you requested already coded and working examples as well, get matlab, along with chan's 'quantitative trading' book for examples. I've posted some emulations using python on another thread.