Well, firstly there is no point in upgrading from the 3570k to the 7500. It's a sidegrade more than anything and will not yield much of a performance boost. FOr the best results in FPS, obviously the way to go is a GPU upgrade. Whilst I wouldn't say that's a bad option (you will get a bump in performance), your current CPU, and the proposed one will bottleneck the new GPU in CPU intensive games. Games like BF V or anything new AAA will suffer with the 4c/4t CPU's you are thinking of.
For being relative, you really need a platform upgrade sooner than a CPU/GPU upgrade for your dated mobo.
If you are gaming on 1080p/60hz, I'd say spend the money on a new platform, keep your current GPU for a while until you can then afford an upgrade, and have a CPU and system capable of giving you what you want.
A Ryzen based system like this:
PCPartPicker Part List
CPU: AMD Ryzen 5 2600 3.4 GHz 6-Core Processor ($117.68 @ Amazon)
Motherboard: MSI B450 TOMAHAWK ATX AM4 Motherboard ($110.99 @ Amazon)
Memory: Corsair Vengeance LPX 16 GB (2 x 8 GB) DDR4-3200 Memory ($79.98 @ Amazon)
Total: $308.65
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2019-11-12 13:53 EST-0500
or Intel system like this:
PCPartPicker Part List
CPU: Intel Core i5-9400F 2.9 GHz 6-Core Processor ($144.99 @ Amazon)
Motherboard: MSI B360-A PRO ATX LGA1151 Motherboard ($90.99 @ Amazon)
Memory: Corsair Vengeance LPX 16 GB (2 x 8 GB) DDR4-3200 Memory ($79.98 @ Amazon)
Total: $315.96
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2019-11-12 13:54 EST-0500
Add your current GPU to this, along with SSD/HDD and then decide down the line to get another GPU. AKA RTX2060 Super.