Thanks for replies and to answer your questions.
I do not plan on upgrading the rest of my build. Would it be necessary in your opinion? I have bought this CPU about two years ago and I thought that it should be enough for a while.
Just to clarify on the CPU cooler, I have this fan but 14 inch big and additional tower radiator or how it is called in english. Do you think I still should upgrade the cooler?
The size of the monitor will depend on some more things. One thing is the final resolution. If it will be 1440p then I would take 27" monitor, if 1080p I would probably take 24" or I would need to somehow try 27" monitor with 1080p to see if it is acceptable for me. I am from Czech republic so I will shop in local market.
My current monitor is Acer G225HQV so it will be a big difference for me. Also, I would probably want to save up as much as I could because there could be more "good" monitors for 1080p for less money than 1440p monitors where I would need to pay more to get some decent quality I think.
EDIT: I might also buy a 27" 1440p monitor and use it at 1080p and maybe wait until new GPU generation comes but I am not really sure I would be able to wait
EDIT 2:
It seems that 2060 Super and 2070 Super are way over my budget in my country. It seems that I should by the 5700 XT Here is what I found.
GPU
For 480 USD:
GIGABYTE Radeon RX 5700 XT GAMING OC 8G
ASROCK Radeon RX 5700 XT Taichi X 8G OC+
GIGABYTE GeForce RTX 2070 WINDFORCE 2X 8G
For 440 USD:
Sapphire PULSE Radeon RX 5700XT 8G
GAINWARD GeForce RTX 2070 TwinX 8G
GAINWARD GeForce RTX 2060 SUPER Ghost 8G
ASROCK Radeon RX 5700 XT Phantom Gaming D 8G OC
Monitor
24" 1080p:
AOC C24G1
AOC 24G2U/BK (probably the best in this category)
27" 1080p:
AOC 27G2U Gaming
27" 1440p:
AOC Q27G2U/BK Gaming - 350 USD
Samsung C27JG56 (and similar Samsung models) - 300 USD and lower
IPS panels start at 370 - 400 USD and go higher:
HP X27i 2K Gaming
LG 27GL83A-B