Well, there is the Ryzen 5 1600. The 2600 basically just has a clock speed advantage and an overclocking advantage. It is still 6 cores and 12 threads. The only other option would be the 2400G. Right now Newegg has both CPUs on sale for $140 and $135 respectively. So... if you got a 2400G and an RX 580 you would come in at around the same price as the 2200G and 1660 combo.
Soooooo, some post-it note math tells me that the optimum price right now for the 2200G and 1660 is $315. Meaning for the exact same budget getting the 1600 leaves you with $170 to spend on a GPU... which is RX 580 territory, but the 580 still comes in at $20 more than budget. The difference between the 1660 and the RX 580 is only about 16%, and the performance gains from the 2200G to the 1600 is measured as 6% by UserBenchmark... however, you gain 2 cores and 6 threads of CPU resources... which is HUGE. So you'll have more CPU performance and only slightly less graphics performance for $20.
Now, you've mentioned that you want to play at 1440p? The GTX 1660 is not a great 1440p card. It is capable of playing at 1440p, then again so are the RX 580 and the RX 570... and you'll have a good time with any of them if you run at medium settings instead of high. These cards are meant for high end 1080p gaming. So they will deliver decent 1440p results at reduced graphics settings. For a card that is capable of 1440p gaming at high settings you need to be looking at more powerful cards like the 1660Ti, GTX 1070, RTX 2060, or Vega 56. Any of those would be outstanding for 1440p at high settings and 60+ fps. The RX 570, 580, GTX 1660, and GTX 1060 are all at best medium settings 1440p at 30-60 FPS cards.
So, for my final CPU suggestion, and this is going to be coming from way off in left field because I haven't even mentioned it yet, it is the Ryzen 7 1700 with 8 cores/16 threads, which is sitting around $160 on Newegg right now. Add to that an RX 570 and you come in at $300 for CPU and GPU. In a year or two you can upgrade to just about anything you want for a video card and the CPU will still be a good performer.