You can most likely play many games if you turn off all the pp effects
i mean just an example it does not look very nice but its playing games.
Tripple A games like COD, counter strike and many others like these set the net wide because they want their games to run on anything so that they can make heaps of money so they will run good on low spec computers etc. Games like Warcraft are in the same boat and also as the other person mentioned RTS games are less taxing so can run on low computers too.
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its a catch 22 because you are asking what good looking games will run but your GPU cannot do good looking in most cases, it will do fuzzy slide show no worries though.
RE5 like you mentioned works well and is a good example of AAA game that will run on anything and play + look good.
Look for games like this its hard to describe if you don't know but most seasoned gamers will know how to spot them. Linear on rail type games are the sort of games you are looking for vs true open world and ones made by big name companies as they will have fast optimized code etc.
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look at easier games maybe like 2D ones there is plenty of fun 2D games and even isometric games as they are often pseudo 3d.
Minecraft can go a long way?
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thanks, it has 20GB RAM, common 3.5" sata hard disks, P8H77-M motherboard
about the concept of modern... it's really relative to one's ability or reluctance to sped for nowadays stuff (which is outrageously expensive for me). For me "modern" is anything done around 2010... usually '09 games are difficult to play at high settings (and logically lame, as I prefer older games)... honestly, everytime I hear the word "modern", my brain hurts, lol
I just want to push the current PC to the best it can.
You are holding this computer back with a GPU like that, you would want to aim for 1080p you could put at least a 780 on it and it will play most games reasonably or well if you know how to min max your setup properly or you could put a 960 or even 980 on it and it will be good for most things.
You could even put a 1660 or a 2070 and up on it and it will do everything all though RTX cards you will be missing some of the feature support because legacy system but they will still work fine and play all games.