Slugster

Here you go, bearing in mind your starting point:
 
You don't need a case, you don't need a PSU, you don't need RAM, you don't need a HD, you don't need an SSD.
 
Ok, it is $67 over budget, but shop around, maybe there is a better deal with be had somewhere on the MB or CPU, or if you really can't find a better deal, go for a slightly cheaper 5700 XT, that isn't the cheapest one around, it is just one I have heard good reviews on.
 
This would be a pretty good system for gaming. 3600 isn't far off the curve and the 5700 XT is pretty powerful.
 
PCPartPicker Part List Type Item Price CPU AMD Ryzen 5 3600 3.6 GHz 6-Core Processor $172.34 @ Walmart Motherboard MSI B450 TOMAHAWK MAX ATX AM4 Motherboard $114.99 @ Best Buy Video Card PowerColor Radeon RX 5700 8 GB Red Devil Video Card $379.99 @ Amazon   Prices include shipping, taxes, rebates, and discounts     Total $667.32   Generated by PCPartPicker 2020-05-26 20:40 EDT-0400    
Oh my last little point to persaude you to the dark side of AMD.
 
This build will last you, it won't last forever, but you will be able to play games that come tomorrow, next year, and you will be fine.
 
The upgrade path you are taking might just about play games today, but you aren't going to be able to keep up, as you are barely keeping up with today's games.

Right now for what I can find, a 7700k is around 380$, so I'm not sure how out of budget you would want to go, but if you would like to put money toward the 7700k and downgrade your budget for your gpu, that would work. Also, with the cpu, while I'm not an expert by any means, its not a bad cpu. If it can still run games well with what you plan to play, and you don't need a big boost in productivity workloads, then it should still be fine. If you are mainly focused on gaming, I would say keep the cpu, and upgrade to a 2060 or a 1660 super, and leave the cpu. If you want to upgrade the cpu and gpu together so you don't have to deal with two separate upgrade time frames, then I would upgrade the cpu to the 7700k, and assuming for pricing right now you buy it for 380$, that still leaves you with around 220 to work with on a gpu. This can be improved by selling your older 970 card, which goes for around 100$ or more used right now on ebay. This means, if you don't mind waiting for a bit for your new card, your budget can be a little higher than previous, at around 320$ for a gpu. If this is the case, then go with the previous reccomendation of a 2060 or 1660 super. If you can find better deals when this happens, then go for those.  This next part assumes you don't sell the 970 card, and just buy for around 220$ for a new card. GTX 1660 cards that are non ti or super are around 200$ right now, some a bit higher around 215$-250$. These are all still good options, especially since the 1660 super only gives a slight bump over the non super 1660 cards. I would aim for around that price point, though there are some good rx590 deals for around the same price, and deliver about the same performance. This link is the improvement from a 970 to an rx 590: https://gpu.userbenchmark.com/Compare/Nvidia-GTX-970-vs-AMD-RX-590/2577vs4033
 
and this link shows improvement from 970 to 1660: https://gpu.userbenchmark.com/Compare/Nvidia-GTX-970-vs-Nvidia-GTX-1660/2577vs4038
 
Again, both of these options assume you don't sell the old card (gtx 970) for a larger budget, allowing you to hit rx 5600xt and 2060 territory, maybe even a good deal on a 2070 if you can find it.

I did a build in another thread for another post, $660 and it had a RT 5700 XT in it and a Ryzen and as I remember it was a full build.
 
So let me see if I can find the damn thing.
 
Price seems to fluctuate up to $670 now, but shop around you could find cheaper and if you have a PC, you maybe don't need RAM or SSD/HDD
 
This was only a 5500 too, memory is shady, but really with the $160 saved on SSD/HDD/RAM you may get the RX 5700 XT

This will be better than any cobbling together you try and do with that motherboard.
 
AND it has an upgrade path, insofar as the B450 boards will support Ryzen 4000 series (though not spectularly easily) but at least you will be able to upgrade in the future.
 
PCPartPicker Part List Type Item Price CPU AMD Ryzen 3 3300X 3.8 GHz Quad-Core Processor $119.99 @ B&H Motherboard Gigabyte B450M DS3H Micro ATX AM4 Motherboard $72.99 @ Best Buy Memory G.Skill Ripjaws V Series 16 GB (2 x 8 GB) DDR4-3200 Memory $69.99 @ Newegg Storage Silicon Power 256 GB M.2-2280 Solid State Drive $34.99 @ Amazon Storage Seagate Barracuda Compute 2 TB 3.5" 7200RPM Internal Hard Drive $58.98 @ Newegg Video Card ASRock Radeon RX 5500 XT 4 GB Challenger D OC Video Card $159.99 @ Newegg Case NZXT H510 ATX Mid Tower Case $69.99 @ Best Buy Power Supply Corsair CXM 550 W 80+ Bronze Certified Semi-modular ATX Power Supply $83.98 @ Newegg   Prices include shipping, taxes, rebates, and discounts     Total (before mail-in rebates) $690.90   Mail-in rebates -$20.00   Total $670.90   Generated by PCPartPicker 2020-05-26 20:26 EDT-0400