I think you underestimate what a PC can do, even your cheap build wild be able to outperform a ps4 in graphics, even play next gen in low graphics in 1080p.
500w is plenty, specially for what you want, I am also researching parts for my PC and 500w is ideal, I made sure I searched for low powered GPU and CPU, I came to the conclusion I can save electricity with Nvidia, which is a shame because AMD is cheaper.
The good thing about electricity on PC is that monitors waste around 20-40w, compared to my projector at 300w.
Now what I find strange is you say the difference between the cheap and expensive build is around 300dollars, but I think its much less, the difference between those graphics cards is only 60 dollars on amazon. The nvidia 1660 OC super with 6GB GDDR6 is around 250dollars brand new, and that will definitely run next gen games. And if you try gta5 on it, you will never play GTA on ps4 again, the difference is massive.
Watts is more than I was willing to go for, its 125w just the graphics.
My big advice to you, wait until the release of next gen consoles, because PC parts will become cheaper/better, there's always a jump in quality and drop in price when new consoles come to market.
January sales are your best bet, or even black Friday if you can wait.
In my case I'm waiting to see the prices of new consoles and such, It might be the first generation that I skip consoles and go full PC, because PCs are fully backwards compatible with thousands of games at much much cheaper prices at much better graphics, example I can play max payne 3 with beautiful graphics, no jaggies on PC, but I would need to buy a 360 to play it and it would look horrible with all the jaggies.
One thing you have to invest in is proper cooling, my brother build his PC recently with my help, we read the reviews saying the graphics was quiet, that's a lie, nowhere near the xbox X or even the pro 3rd revision, PCs get really loud if you max out graphics, my brother ended installing water cooling, so you need to look into that if you are bothered by noisy fan.
