It's easy enough to have your home page set in Opera, and then to have a home page button.
To set the home page so your browser opens there, just go to Settings in the Menu (Alt P), and select your home page location.
Now to have the button/icon, download the extension, Homepage in New Tab, which sgunhouse has pointed out and I've tested. https://addons.opera.com/en/extensions/details/homepage-in-new-tab/?display=en
It will put a homepage icon/button on your icon bar (to the right of your address bar). Now go to a webpage with the address you want for your homepage, right click on the address and copy it. Now right click on the homepage icon on your icon bar, click on options, and paste the address you want for your home page into the Homepage setting. Now every time you click on the icon for Homepage, you will return to the homepage. When you open the browser, you will be at the home page. If you click on the plus symbol, you will add a tab that is the speed dial.
The custom home page extension (that sgunhouse also mentioned) didn't seem to give me the icon on my icon bar. You did say you wanted a toolbar button, and the icon is as close as one can get to a button.