Do you own any parts now?
If so, what is the make/model of each.
Include psu, case, monitor, drives
To answer your question, NO, a FX-4300 is not worth spending a dime on.
As to gaming at 1080P. what kinds of games do you play?
A balanced gamer will budget 2x the cost of the processor for the graphics card.
If you play fast action shooters, spend more on the graphics card.
If you play sims, strategy and mmo spend more on faster single thread performance.
If you play multiplayer, spend more for more processing threads.
Actually, with the recent 10th gen intel announcements, now is not a good time to prematurely buy.
Intel is going to be competitive.
Since you are replacing a pc, you can keep the windows 10 license.
You need to register for a microsoft account .