Your PC specs don't make that much of a difference in choosing a monitor. What makes a difference is what you want from your monitor. Do you want it to be 4k? Do you play a lot of competetive games? If you do, you might want to consider a high refresh rate monitor. Does colour accuracy matter to you? There's all kinds of monitors and most of them display images just fine. So if you don't want anything specific just get the cheapest or the most aesthetically pleasing one you can find.
Oh and you said "upgrade" in your post, don't throw away your old monitor, you can still use it as a secondary display. Having more than one is great.