I see this is a couple months little old, but probably still worth commenting.
First, looking at bela schematic the input impedance is too low for direct connection to a guitar for good guitar tone (looks like 80k on TI CODEC inputs). You want something >500k, preferably 1Meg. A simple JFET buffer can be added to the input. Just google "simple JFET guitar buffer" and you will get lots of hits with projects.
Even though the input resistance is a little low for guitar use, it will "work", so it's not absolutely necessary to build a front-end buffer, but definitely a good idea if you want to get the best guitar tone out of it. It's probably a good idea to have an amplifier with a level meter on the output (at the very least a clipping indicator) so you can adjust the input level for optimal use of the ADC full dynamic range. A level meter can also be implemented in software and used to drive IO pins if that is preferred.
Some years back I contributed a lot of code to the open source project Rakarrack:
The project has pretty much died but its main objective was accomplished: port ZynAddSubFX synthesizer effects to a guitar-friendly interface. There's a lot of useful DSP code in that project and in my mind pretty straightforward to implement on any generic platform. If you don't know any C++ then you will have that hurdle for a while.
Either way I intend to start implementing some guitar effects on bela using C or C++ (depending on the mood I'm in that day -- I generally prefer plain C). I will most likely make it public domain or GPL when I get there but it will probably be a while. I'm running a delay/flange/chorus (modulated delay line) chain of effects in C on a Raspberry pi right now, but Bela makes the audio IO and user control much better suited to the ultimate goal of a guitar pedal.
Should be plenty of horsepower for the basic stuff (flange, chorus, echo, phaser, envelope filters, basic distortion, wahwah, etc). Stuff like @matthieub suggests starts to enter a level of processing that could push the limits of the beaglebone black.