You can do all this in Semiautomatic Classification Plugin (SCP) and you can also do a quick (and simple) atmospheric correction with SCP. Regarding the data: Sentinel A-2
In my opinion, SCP is one of the very best plugin available today for QGIS.
About the QGIS Semiautomatic Classification Plugin, Luca Congedo (developer) do a very good support. I recommend contacting Luca to inform him of the question.
For the crop classification, instead of landsat you may check https://sentinel.esa.int/web/sentinel/user-guides/sentinel-2-msi
Instead of searching software, please specify your purpose as you may need high resolution of spectral or spatial features. As sentinel-2 data have rededge spectral bands, it may be more proper for agricultural missions however again need to say it is reallu up yo your application of what you wish to do.
Another advice is just add vegetation indices or textural features into your classification step then probably it can help you to discriminate the classes of interest into your area.
Now, my advice is first meet the data and spectrally analyse it ( means complete the proper processing before the classificaion) then start processing the data.
ESA has free tools as one of them are SNAP where you can find the classification tools.
You can also check links for tools help you for classification as below: