We spend a lot of our time developing code for experiments and data analyses (mostly in MATLAB). Here are some of the toolboxes and apps we find helpful:
SPM for preprocessing MRI data and GLMs
FreeSurfer for surface reconstruction
SamSrf for fitting encoding models (e.g. population receptive fields)
Psychtoolbox for stimulus presentation and data recording
Custom code: we're committed to publishing our code and data wherever possible. For individual projects, check out the publications page and OSF. Ben also published some utility functions, which you can find here.
Textbooks & tutorials
Some of the links above include learning resources for the respective packages. For neuroimaging analyses we recommend the excellent Handbook of Functional MRI Data Analysis by Poldrack et al. and Statistical Analysis of fMRI Data by Ashby. To get into MATLAB, we recommend MATLAB for Neuroscientists by Wallisch and colleagues.