It's worth downloading the mobile app for some extra peace of mind. Google Photos offers truly unlimited backup of all the photos (and videos) you take. Every single one. The caveat: they have to be less than 16 megapixels to qualify for the unlimited storage. You are allowed to upload larger images—but Google converts them on the fly to 16 megapixels. (It downgrades video shot above 1080p.)
There is also an option to upload images at "original" size. If you pick that, images are not converted, but they count against your allotted 15GB of online storage with Google, which is shared with Gmail, Google Drive, and other Google services. (Naturally, you can pay Google to get more storage at $2 per month for 100GB extra or $10 per month for 1TB.)
Google Photos came about by salvaging the best part of the Google+ social network that no one wanted to use—the photo storage and sharing. Sadly for some, Google Photos also replaced our former Editors' Choice photo software Picasa, the desktop program that Google acquired way back in 2004. If you used the Picasa Web Albums for any online storage, all your images have been shunted to Google Photos. You can still use the Picasa Desktop software if you have it; but it'll never get an update, nor can you get support from Google if you have a problem. It's probably time to let it go.
To be honest, you won't miss it, if you are willing to leave desktop programs behind. Google Photos was built from the get-go for use on mobile devices via apps (iOS and Android) and on the web. On iOS, it even supports Live Photos.
It's far from perfect; if you want really unlimited storage, Flickr users get a free terabyte. However, like most online services/apps, Photos adds new features all the time. Many are meant to automate your use, some of which we'll cover here. Read on for all the little tricks that will allow you to get the most out of your account.