Visual Studio is not available on Linux and not really working in Wine, sadly. You can use IntelliJ IDEA as a good alternative, it supports Linux officially and has a Flutter plugin.
For a beginner, Linux Mint is perfect. It is based on Ubuntu which is based on Debian, so you can follow most tutorials written for either distribution (like the installation instructions for IntelliJ IDEA or other software that is not available from the APT package manager).