Show Inbox when starting Thunderbird
From MozillaZine Knowledge Base
Usually if you go to "Tools -> Account Settings -> Account Name -> Server Settings" and check the box that says "Check for new messages at startup" Thunderbird will start in the Inbox folder. If you have more than one account, Thunderbird will start in the Inbox of your default account, which is the account displayed at the top of the folders pane. To make another account into your default account, go to "Tools -> Account Settings", select the account you want to make the default, and click the "Set as Default" button.
However, that doesn't always work in recent versions. There are a couple of add-ons you can use as workarounds.
If neither add-on works around the problem it might be because you changed mail.server.login.at.startup , which defaults to true. 
Opening some other folder
You can also specify any folder as the startup folder (it doesn't have to be an inbox) by changing the command used to start Thunderbird. For example, the command might be in the properties of an icon on your desktop. At the end of the command, add
If you are using Windows 10 right click on the Thunderbird shortcut in the taskbar, then right click on "thunderbird.exe - Shortcut", select Properties from the list box, and select the shortcut tab (if it isn't selected by default). Find the target field and add -mail, a space and the URI of the folder.
For example, if you want to open the inbox folder for a gmail POP account:
"C:\Program Files\Mozilla Thunderbird\thunderbird.exe" -mail mailbox://email@example.com/Inbox
If you want to open a Templates folder in the same POP account:
"C:\Program Files\Mozilla Thunderbird\thunderbird.exe" -mail mailbox://firstname.lastname@example.org/Templates
If you want to open the inbox in the Local Folders special account you need to use double quotes due to the embedded space:
"C:\Program Files\Mozilla Thunderbird\thunderbird.exe" -mail "mailbox://Local Folders/Inbox"