You’re going to want a high-speed connection with upload and download speeds of at least of 5Mbps to get the best experience. Ideally, your PS4 should be hooked up to the internet with a direct ethernet connection, and the same goes for you PC or Mac.
Having said all that, I managed to tether my 4G smartphone connection to a laptop which provided a smoother experience than the office Wi-Fi. Thank goodness for all-you-can-eat data.
You should also kill all downloads or other apps which could be taking up bandwidth, and feel free to tweak settings like the resolution and frame rate in the PC and Mac Remote Play app preferences.
Even with a decent connection, you might still encounter small delays which could negatively impact your performance it twitch shooters like Call of Duty. The best experience I’ve had so far is with Rocket League, managing to net a hat trick without much fuss. #humblebrag
And there you have it. Amaze your friends. Perplex your peers, and never get anything productive done, ever again.