Abigaroth

Since your goal is I'm assuming to even utilize that 144Hz monitor then buying either a new GPU or CPU won't benefit you in any way since the FX 8320 + R9 380 can already achieve above 60 FPS in DOOM and because your monitors are 60hz you won't notice a difference, I would go with the monitor upgrade, and then CPU and then GPU.
 
I would also suggest to hold off on the GPU upgrade and wait for the new GPUs to come out this year.
Yes the FX 8320 would bottleneck the hell out of the 5600XT, you most likely won't notice any performance improvements over the R9-380 if you do so.

Monitor upgrade should be the last thing you do tbh, unless you upgrade everything at the same time, since with your current CPU but a better GPU you'll barely see any gains, and with a new CPU will get something extra from your GPU but not enough to justify a 144hz monitor.

that fx is not good just get new cpu
PCPartPicker Part List Type Item Price CPU AMD Ryzen 5 3600 3.6 GHz 6-Core Processor $172.39 @ Newegg Motherboard MSI B450 TOMAHAWK MAX ATX AM4 Motherboard $114.99 @ Best Buy Memory Patriot Viper Steel 16 GB (2 x 8 GB) DDR4-3733 Memory $87.99 @ Amazon Storage Crucial P1 500 GB M.2-2280 NVME Solid State Drive $59.95 @ Amazon   Prices include shipping, taxes, rebates, and discounts     Total $435.32   Generated by PCPartPicker 2020-05-05 04:28 EDT-0400   after that upgrade to 5600 XT. keep that ips monitor. IPS is the best panel out there. 1080p 144hz ips is pretty good

I'd say go the motherboard + cpu route, but you'll also need a new kit of ram since your old socket mounts DDR3 and you can't use them on the new one

TN panel is shit. atleast get VA panel.

Thanks! i will start to save money to buy MB, Rams and CPU. I will need around 540USD to buy all here at this 3rd world country.