Yeah, I wouldn't get an expensive cooler for these CPUs. Even if you want the CPU to be quiet when overclocking, you could do so on a 120mm tower cooler priced around $35 or less.
And like Froggy said, there are lots of 24 inch 144Hz monitors priced around $180 or less, so they're definitely worth considering, especially for competitive multiplayer games where you could push high frame rates with a graphics card like this. I would look for one that supports FreeSync though, as both Nvidia and AMD support adaptive sync on FreeSync monitors now. Just make sure the monitor supports FreeSync over a DisplayPort cable for Nvidia cards, and you should be able to enable "G-Sync" from Nvidia's control panel.
I tried my hand at a build suggestion as well. In this example, I ditched the mechanical hard drive in favor of moving up to a 1TB SSD. 1TB mechanical hard drives are priced poorly relative to larger capacities, so they're not worth including alongside an SSD, in my opinion. If you need lots of bulk storage for video or an extended game library, move up to at least a 2TB hard drive for just a little more. Otherwise, you can put the money toward getting a larger SSD, where you will probably want your games installed for faster load times.
I also included a 750 watt Seasonic Focus Plus Gold PSU. You wouldn't actually need anywhere near that capacity, but it's possible to get it for less than the cost of lower capacities at the moment (at least after rebate). If you don't want to mess with a rebate, the 550 watt model would be perfectly fine though.
As for the peripherals, I went with the mouse you selected, though there are a lot of options around this price range. I did move up to a proper mechanical keyboard with brown switches though. This one has red backlighting, though if you don't like that there are some mechanical keyboards with RGB backlighting around this price range as well. Or ones with no backlighting, for that matter. : P
Also, I had it just under your budget, but then decided to swap out the motherboard I had listed for one with better reviews for about $15 more. So, it's slightly over budget now. You might also need to figure sales tax into the prices of these builds, depending on where you are located, if you want to keep it under $1100.
PCPartPicker part list /
Price breakdown by merchant
CPU: AMD - Ryzen 5 2600 3.4 GHz 6-Core Processor ($164.89 @ OutletPC)
Motherboard: Asus - PRIME B450M-A/CSM Micro ATX AM4 Motherboard ($79.99 @ Amazon)
Memory: Crucial - Ballistix Sport LT 16 GB (2 x 8 GB) DDR4-3200 Memory ($89.99 @ Newegg)
Storage: Intel - 660p Series 1 TB M.2-2280 Solid State Drive ($114.99 @ B&H)
Video Card: Gigabyte - GeForce GTX 1660 Ti 6 GB OC Video Card ($274.99 @ Amazon)
Case: Phanteks - Eclipse P300 Tempered Glass (Black) ATX Mid Tower Case ($59.99 @ Amazon)
Power Supply: SeaSonic - FOCUS Plus Gold 750 W 80+ Gold Certified Fully-Modular ATX Power Supply ($69.99 @ Newegg)
Monitor: MSI - Optix MAG241C 23.6" 1920x1080 144 Hz Monitor ($179.99 @ Newegg)
Keyboard: G.Skill - Ripjaws KM570 Wired Gaming Keyboard ($59.99 @ Newegg)
Mouse: Redragon - COBRA M711 Wired Optical Mouse ($19.89 @ Amazon)
Total: $1114.70
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2019-03-26 15:19 EDT-0400