For example, I would like to use scikit-learn for machine learning, and pandas, numpy, and matplotlib/seaborn for data analysis. Does AWS Lambda support all these libraries? Is there a list of libraries supported? Or should I create a virtual server instead, to ensure I can use any Python library I want?
Those modules are not available by default. I found this (older) list of available modules, along with code to generate a current report of what is available, should you wish to do so:
https://gist.github.com/sjehutch/36493ff674b1b9a16fc44a5fc270760c
You can build your own environment using a virtualenv and upload that to Lambda. It can contain anything you want. See here for more info:
https://docs.aws.amazon.com/lambda/latest/dg/lambda-python-how-to-create-deployment-package.html
So you can still use AWS Lambda, and should not require a virtual server.
Edited to add a bit of self promotion:
I made a web site that shows the current modules available in each environment provided by Amazon.
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