gmail does not allow to things that a regular email client do, so, thunderbird is a good option.
But ThunderBird does not have a minimize to tray option. There are plugins but I read around forums and they have problems depending on the version, so, I wrote a non-plugin solution to my wanting.
Sources and compiled executable files are at https://www.autoitscript.com/forum/files/file/438-thundrebirdtotray/
The tray icons are:
Pruple = ThunderBird is not running. A double click will run it.
Blue = ThunderBird is visible. A double click will hide it
Green = ThunderBird is hidden. A double click will unhide it.
Right click will show a menu to:
Minimize to tray.
Show/hide ( just as a double click on the tray icon would )
Compose a new email.
Browse some folders that may be of interest.
In new version 0.2017.3.11
added: command line options /RunAs "UserName" [/minimized] [/hidden].
the user/password is saved encrypted to the ini file to each user's configuration.
fixed: "dyslexia induced" misnamed files.
added: browse startup folders
PS: I run this from "C:\Program Files (x86)\Mozilla Thunderbird" but I guess you can run it from anywhere. The features implemented are those to fit my needs. If you'd like to add a feature, I could go the extra mile line of code and add it. You may even make me aware of things that can be done, and be of use, that I did not know at the time of coding this.