It's something you have to judge for yourself after trying. You don't need constant 144 fps to take advantage of the higher refresh rate, you'll feel a smoother experience regardless. For PUBG & Rocket League it won't be that hard to drive tbh, esp. at 1080p. 1440p will look crisper but I can't say the difference is big in any way. Go to TFT Central and look through their reviews for monitors before making a decision. Ideally you'd want a Freesync monitor to keep costs down but that won't work with the 970, which would be enough for 1080p 144hz for the most part, so it would be more for the future or if you'd like to upgrade (maybe if £299 Vegas appear again this Xmas).
Imo with a Vega 56 & a 1440p 144fps monitor you'll be set for years now, esp. in these not as demanding titles, though a 580/590 would work well too - it's just that the jump from the 970 to the latter cards isn't as big. If I were in the market for such a monitor I'd look at the Asus MG279Q. One of the reviews on it, also with a 970:
How can you say there is no big difference between 1080p and 1440p? It made a massive game-changing difference for me. I could not go back to 1080p now, it just looks and feels so old and blocky by comparison. 1440p is the sweet spot for me, one of the best upgrades I have ever made OP. I would highly recommend it.
And no you do not need to be getting 144FPS, it is noticeably smoother anyway.