If its oldschool FPS gaming that you seek, you might want to take a look at the recently released arena shooter Reflex. It features a wide array of powerful weapons, an intense focus on speed and precision, and naturally, plenty of ways for personal skill to shine.
Since trying to explain something like this through words alone is a pointless venture, allow me to share with you the launch trailer. It briefly goes over all of the important features, and it showcases plenty of pure gameplay, so you should get a good idea of what Reflex is all about. Have a look:
What I personally find the most interesting about Reflex is the inclusion of a proper in-game map editor. Not only is this good for Reflex's longevity as user created maps tend to be the best ones around, but its also great for new players because of the various practice maps - something I find even Overwatch to be sorely lacking in. And since Reflex has been in Early Access for a couple of years now there are quite a few maps to choose from, including nearly 90 training modes!