The issue is that I have a 4k monitor and my current card can barely handle my desktop, never mind a game.

Try running games at 1080p (1920 x 1080), which is exactly 1/4 of 4K UHD (3840 x 2160). Your graphics card will only need to do 25% of the work but you shouldn't get any resolution scaling blurriness because everything divides evenly. This isn't so much for your current card, which probably just can't keep up with newer titles. What you can do is look at 1080p performance of current cards, decide how much performance you need and how much you're willing to spend, and that'll narrow down the selection a lot.

Coming from a GTX 760, almost anything current gen or current gen minus 1 is going to be a massive upgrade. It's hard to recommend a specific card without some info on your budget. For example if you had a budget of $300 US I'd recommend an Nvidia RTX 4060 since it has the best 1080p performance within that budget, or alternately a Radeon RX 7600 if you'd prefer not Nvidia (e.g. if you're on Linux, the Radeon driver story is a bit better).