I am looking forward to working on GEE using Python but need suggestions as to where to start from; I can't find much info on Python API for GEE. The other APIs (like geemap) is more convenient on Google Colab or Jupyter notebook?
GEE itself a cloud computing platform and frequently used as a standalone application. The number of built-in functions are exceptionally large.
"Google Earth Engine is also available via a Python Application Program Interface (API). Users can write and execute python code in any editor they prefer and in any environment. Access to Google Earth Engine is currently only available to registered users. The API is in active development, and users should expect the API to change."
Colab Integration with GEE seems pretty good as both are own by Google. I think if your computing power of PC is not good enough, working with large data would be problem using Jupyter Notebook. Secondly, Colab Notebook is much similar with Jupyter NoteBook, most of the functionality can be called in Colab. e.g. Machine Learning etc. Finally, you can do some personal assessment through several experiment with data to reach at final conclusions.
There is no such thing as a completely perfect situation. Everything has advantages and disadvantages, and which you prefer is a matter of personal preference.
Google colab: useful for collaborative online work with multiple members; it's also useful if your system is slow and you want to run heavy programmes on your computer ( cause it processes on the cloud).
Jupiter notebook is an offline, on-system integrated development environment (IDE) for programming. It performs admirably and even includes features for working with a group of people. It has the ability to access and use the files on your system as well.
In my opinion, jupyter notebook outperforms Google colab in terms of functionality. However, if you are concerned about the performance that you are getting from Google colab, or if your system is slow, you should consider using Google colab instead.
i recommend you the Jupiter notebook because this tool very effective. for python scripting and coding, you need to achieve the good results at least install the python package library.