If you play a note on a guitar, what is the main note that you hear?
It's certainly not necessarily the loudest one. You might want to read the Wikipedia articles on "pitch" and "missing fundamental" for an understanding of how we interpret musical sounds. The relationship between frequency - a physical property - and pitch - a perceived property - can be complex.
What I want to do is
- take an input signal from a bass or guitar,
- find the fundamental frequency of it, and then
- store that as a variable.
Because you tell us this:
... I am pretty competent in programming ...
I'll presume that you don't need any help storing a result. I think that you're looking for help with the other two tasks on your list: collecting analog samples from an audio input, and processing those samples to estimate the frequency of the audio signal.
Collecting samples has elements of hardware design and programming, while processing those samples is strictly programming. If you start with the task of processing samples, you can go a long way toward your goal without having to design hardware, by processing calculated analog values as opposed to analog values acquired from an audio input. Designing the hardware interface between the Arduino and the audio signal will require a fairly thorough understanding of the characteristics of the input hardware. Whichever task you tackle first, you'll want to use calculated values for testing the algorithm that estimates frequency, so that you can easily predict the correct results. Ultimately, though, you'll have to get both tasks working to make this project work.
I think that your project is achievable with an Arduino Uno, or maybe some derivative. But, it's certainly not trivial.
Which task do you want to tackle first?