GMail has a built-in desktop notification system you might want to try. Once you turn it on, you just have to leave GMail open (minimized on your taskbar is OK) and the notifications will show and play a sound (if you wish) whenever there's a new email message in your Inbox.
This is the information from
Change email notifications - Computer - Gmail Help:
Turn Gmail notifications on or off
You can get email notifications on Google Chrome, Firefox, or Safari when you're signed in to Gmail and have it open in your browser.
On your computer, open Gmail.
In the top right, click Settings and then See all settings.
Scroll down to the "Desktop notifications" section.
Select New mail notifications On (or Mail notifications Off).
At the bottom of the page, click Save Changes.
Leave GMail open, but leaving just the icon on your taskbar is OK.
You can select a sound, or select No sound.
If you need any help setting this up, post back here, and I'll try to help.