Need help Upgrading My Pc

Gpu is a must. Your current gpu is very low on the ability scale compared to what the games are requiring nowadays.
Cpu. That's tough, because the i5-3570k is still a respectable cpu, especially for your current needs, but games are making use of more than 4 threads an i5 is capable of. A cheaper solution would be to hunt down an i7-3770K on ebay, then see about some OC as your cpu and mobo are quite capable of that. This would include a decent cpu cooler.
Ram could be improved to 16Gb, you'll maybe not use more than 8Gb, but better to have it and not need it, than to need it and not have it.
Cpu and mobo and ram. If you upgrade to more current, you'll need new of all 3. Newer cpus do not work on older boards, your board is lga1155, new stuff is lga1151, physically incompatible. The new stuff uses DDR4 ram, not the DDR3 you currently have, again physically incompatible. Quite easy to spend $400+ just in those 3 together.
SSD if you don't have one, your pc might seem slow by comparison. Not really needed, but anything that saves time sitting and waiting for things to load just makes a pc seem much h faster overall.

Just buy yourself a GTX 1060 6GB card and you should be good to go.

Since this is a gaming PC, it is more dependent on the GPU, but which consequently needs a good CPU for the GPU to be able to perform to its maximum potential.

As of the above recommendation, the i5-3570K + GTX 1060 is already a good pair, so, any upgrades on the CPU is not worth it in my opinion (for a GTX 1060 GPU). Add to the fact that you have a 3rd-gen Intel platform with a top-of-the-line i5 "K" (overclockable) CPU meant for gaming, which limits your CPU upgrade choice. Upgrading to a more powerful i5 necessitates going to a next higher-generation, which means, a new platform (new MB, and RAM). Upgrading to the same-gen (3rd-gen) i7 "K" CPU would not give you much benefit in terms of gaming, so, it's money not well spent.

RAM is the only logical choice I can think of upgrading IF you decide on retaining that 3rd-gen platform for a longer time. Nowadays, those DDR3 aren't/can't be used anymore in current-gen builds (7th-gen Intel and Ryzen AMD builds), as these new builds require DDR4. The 8GB RAM you have is still considered an "okay" capacity for gaming (it's considered nowadays as the minimum, but depending on what games you play). Some opt for 16GB RAM for the recommended specs requirements on certain games, but, not all games utilize that much RAM (only if your PC is used for multi-tasking/workstation use that the 16GB may be beneficial).

Some might find adding an SSD will increase performance (but only in desktop use and loading times, not much in actual gaming).

So, with the above considerations, if you really really want to upgrade, just upgrade the GPU, and I would save the rest of the money for a new platform if you want to get the best price/performance, instead of upgrading certain parts of your already gaming-oriented 3rd-gen CPU/MB/RAM.

Upgrading from an i5-3570K to a 7th-gen 3.8GHz i5-7600K (costs ~$230) will have ~25% increase in gaming performance: http://cpu.userbenchmark.com/Compare/Intel-Core-i5-7600K-vs-Intel-Core-i5-3570K/3885vs1316

Upgrading from an i5-3570K to a 7th-gen 4.2GHz i7-7700K (costs ~$330) will have ~30% increase in gaming performance: http://cpu.userbenchmark.com/Compare/Intel-Core-i7-7700K-vs-Intel-Core-i5-3570K/3647vs1316

Note that in the above suggested 7th-gen Intel CPUs, you will have to get a new Z270-chipset motherboard (costs ~$110 to ~$200), and a new set of DDR4 RAM sticks (2x4GB 3200MHz costs ~$80 to ~$100; 2x8GB 3200MHz costs ~$100 to ~$130).

Alternatively, you can also upgrade to an AMD Ryzen build. The core speed is a bit less than those Intel CPUs, but the costs are much cheaper (3.5GHz Ryzen 5 1500X costs ~$185). AMD motherboard (B350-chipset costs ~$70 to ~$120). DDR4 RAM costs the same as the Intel build above.

In any of the above builds (7th-gen Intel i5/i7 or AMD Ryzen 5), you can re-use your that Corsair TX750 PSU, your HDD/SSDs, and the GTX 1060 6GB GPU that you will buy.

There's little actual need to upgrade the CPU/MB/RAM, they're fine, if you MUST upgrade, pop over to E-bay or Craiglist and move up to an I7, but only if you're playing the latest, CPU intensive games.
Where you SHOULD be spending is on a faster graphics card, A GTX1060 is going to be a night-and-day improvement over the current HD69XX and if you're using either a 1440 monitor or a fast (120Hz or over) display you might want to look at the GTX1070, or even 1080 if you're on a 1440 display.
For speed: https://pcpartpicker.com/user/coozie7/saved/#view=2Yg6hM

Aesthetics can also play a role. It's quite easy to get a better case, one with a window, maybe some leds or led fans, color match your gpu to existing parts, get a good cpu cooler and OC it till it screams. Basically make the whole pc look like it's better, newer, stronger, faster, even though in reality, cost is minimal other than the needed gpu. There's a lot to be said for being happy with your pc vrs just content that is better.