I want to share experience in the selection of fonts for the site, and I’ll start, perhaps, with the simplest tool.
The easiest tool for working with web fonts is Fonts.google, it’s easier, probably, nowhere. You just need to select the desired font and connect it to the site, and a user-friendly interface will help you determine the choice. Also I recommend downloading their entire collection to work with the site layouts. The simplest algorithm in working with fonts for the site: at the design stage of the layout, you need to select one font from this collection, and when you make the layout, just connect it. Of the amenities on this all, then follow the significant disadvantages:
Google does not work well or does not work at all in some countries,
the speed of loading the page will decrease, since the font is on a third-party server,
a collection of Cyrillic fonts and in fact all except the Latin alphabet, a small one.
For the selection of really high-quality fonts I recommend Wordmark
An excellent resource with a user-friendly interface and cool fonts. The resource can be used as a basis for working with websites and any other graphic tasks. To use it, you will need to spend a little, but the price there is quite modest and will not hit your pocket. In any case, the site is used by many for inspiration, and the font you like can be found on the Internet for free.
Ok, we now have two resources with fonts. But what if you liked the font, but do not know how to find it?
Everything is very simple! It is enough to make a screen or a photo of the font and upload it to the WhatTheFont site. WTF decrypts your photo or screen and selects the most similar fonts. A large database allows you to almost always find the same font.