Players of eSports games generally are dissatisfied with 600 fps. In shooters a high frame rate can make the difference between life and death, especially in the competitive scene. Games that rely less on reaction speed and more on strategy, such as Dota 2, are an exception to this rule, however some pros still swear by high fps.
In general the competitive games that we've tested so far do not strain your hardware that much. The 60 fps can easily be passed with a low-end graphics card, a good middle-class card will generally get you close to maximum frame rates. If you're planning on playing this type of game, the Nvidia GeForce GTX 1060 and AMD Radeon RX 580 are excellent choices. If you're gaming on a budget, you can also go for a cheaper card without sacrificing too much performance.
Investing in e.g. a GeForce GTX 1080 Ti is rather pointless for this type of gamer. The increase in performance compared to mid-range cards is rather limited due to bottlenecks created by the CPU or another component. If you have some money left in your budget, we'd recommend going with a faster processor instead of a more expensive graphics card. You could also just save some money. What's more, a faster monitor or more accurate mouse is very useful in the average eSports game, so spending a bit more on your peripherals instead of the on the components.of your pc does not sound like a bad plan.