What encryption algorithm is better to use? client-Delphi, server-Python. Recommend please simple algorithms and libraries ..
This question is far too open ended.
Your best bet for using the same library in both Delphi and Python is mcrypt. It contains a sizable cipher suite. I recommend AES / Rijndael for just about everything. It's a nice block cipher and is used almost everywhere.
If you are looking for simple algorithms (not simple encryption) then two come to mind:
Both are really simple and could be easily implemented in any language and both are very fast. XTEA is also secure. At least if you are not looking to protect national secrets :) I have an XTEA implementation for Delphi that works under newest delphi versions. Look here.
I also found a Python version: http://code.activestate.com/recipes/496737/
You can also try the Delphi Encryption Compendium. It features the most popular algorithms and is quite easy to use due to it's OO layout.