Yep, it looks like that screen should support 60Hz input at 4K, provided you use the HDMI 2.0 ports (it appears to have one or more 1.4 ports too) but again, you will likely need a new graphics card for that.
Around the $400 level, assuming you are looking at US prices, there is the Nvidia RTX 2060 SUPER and the RTX 2070, along with the AMD Radeon RX 5700 XT. The RTX 2070 SUPER is typically around $500.
In terms of performance, the standard 2070 is only slightly faster than the 2060 SUPER (no more than 5%), so I wouldn't pay more than $20 extra for one. At close to the same price it should be the better option though. The 2070 SUPER should be around 10-15% faster than the standard 2070, though whether that's worth close to $100 more is up to you to decide.
The Radeon 5700 XT costs about the same as a 2060 SUPER or 2070, but is typically a bit faster on average in today's games. There's also the 5700 (non-XT) for around $350, with performance just a little behind the 2060 SUPER. The Nvidia 20-series cards do support some extra features like hardware acceleration for raytraced lighting effects not present on the 5700 and 5700 XT though, but even with acceleration, enabling those effects causes too much of a performance hit to be practical on today's graphics cards at native 4K resolution. It's more of a feature for 1080p rendering at this time. Though again, having games upscale from a lower resolution like 1080p or 1440p is a feature you may still want to utilize with the most demanding games, and both AMD and Nvidia have recently added sharpening options in their drivers to help restore some of the sharpness lost from upscaling.
And compared to a GTX 760, these cards around the $400 price point should offer at least several times the graphics performance at higher resolutions, so any of them should be a substantial upgrade over what you have now.
As for the PSU, I haven't really heard of that brand, so my guess would be that it's probably not particularly good. I would be mainly concerned about it potentially failing and wrecking a $400 GPU.