Any specific games you want to play and any specific performance requirement such as playable or playable with ultra graphics and 60+ fps?
If your games are not that demanding and regular graphics settings are fine, then more money can be invested into a better CPU vs cutting corners on a CPU as a means to include a better GPU.
I have been having pretty good luck using middle range video cards that are inexpensive that can play the games for say 2 or 3 years before a newer game title requires a better video card in which the same system can just get an upgrade to the next best mid range video card inexpensively. I have also bought high end video cards used for like 25% of the cost new which are someone elses prior gaming card which are generally better performance for the same money as a new mid-low range video card.
Have you considered buying any of your parts used to save money vs new, and do you want Intel or AMD for the CPU?