In any case, I came back and tried my hand at a $1000 build here...
PCPartPicker Part List
CPU: AMD Ryzen 5 3600 3.6 GHz 6-Core Processor ($194.79 @ OutletPC)
Motherboard: MSI B450M PRO-VDH MAX Micro ATX AM4 Motherboard ($83.98 @ Newegg)
Memory: G.Skill Ripjaws V 16 GB (2 x 8 GB) DDR4-3600 Memory ($84.99 @ Newegg)
Storage: Intel 660p Series 1.02 TB M.2-2280 NVME Solid State Drive ($94.99 @ B&H)
Video Card: Gigabyte GeForce RTX 2060 SUPER 8 GB WINDFORCE OC Video Card ($399.99 @ Amazon)
Case: Phanteks P300 ATX Mid Tower Case ($59.98 @ Newegg)
Power Supply: SeaSonic FOCUS Gold 550 W 80+ Gold Certified Semi-modular ATX Power Supply ($81.99 @ Amazon)
Total: $1000.71
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2019-09-23 17:43 EDT-0400
I went with the Ryzen 3600 for this build, along with a B450 motherboard that should support 3000-series processors without requiring a BIOS update. I did stay with the stock Ryzen Stealth cooler, but that should be fine for this processor unless you want something that stays a little quieter under load.
I also went with faster 3600 CAS 16 RAM, though cutting back to 3200 CAS 16 wouldn't affect performance too much if you wanted to save an extra $11-$12.
The SSD is the same in j3ster's build, and should offer good performance for its price, being the lowest priced NVMe model available from a decent brand.
The PSU is a good model from Seasonic that should offer plenty of capacity for these components, which are not likely to ever draw more than 350 watts under load.
And the case is just a decent, nice-looking inexpensive model from Phanteks that fits within the budget. I'm not sure whether or not it has better airflow than "some random case that doesn't have great airflow", but it looks nice with tempered glass, and has decent build quality. It could of course be switched to any other case.
I did manage to get a 2060 SUPER 8GB in there, which should push up to 15% higher frame rates than a standard 2060 6GB, or around 40% higher frame rates than a 1660 Ti in games where performance is limited more by graphics performance, rather than the CPU. It would be nearly 3 times as fast as a GTX 680 in such scenarios. You could of course cut back to a regular 2060 for around $330 if you wanted to save $70 though. Or a 1660 Ti for around $270.
However, I notice that you mention getting "144 fps in most games with a 60hz monitor". If that's the case, I'm not even sure you need a new system for the games you play. After all, that 60Hz monitor will only be updating the image 60 times per second, making such high frame rates kind of pointless. Is it even a 1080p screen? Are these mostly e-sports or somewhat older titles? It would actually probably be worth getting a 144Hz high refresh rate and/or higher resolution monitor, and spending less on other components.
It might even be worth just upgrading your existing system for the time being. What are the system's full hardware specs? Does it have an SSD? In what way is your PC "a bit laggy"? I also now notice that you mention it only having 4GB of RAM, which is probably the main cause of that "lagginess". Modern Windows versions will typically utilize a couple gigabytes of RAM just for the OS, so the system will be swapping data out to the hard disk when trying to run just about any semi-modern games. For most recent AAA games, you'll want the system to have 8GB at the very least. It's likely that the system would be a lot more responsive just by swapping out your existing RAM for an inexpensive 2x4GB kit of DDR3 for around $30 on the used market, or around $50 or for a 2x8GB kit. Then just get a SATA SSD for around $100 or less to install Windows, your applications and your most-played games on, and a 144Hz 1080p monitor (which are around $200-$250), and you could likely breath some new life into that system for under $400. The SSD and monitor could of course be carried over to an eventual new system, too.