Which part of my computer should I upgrade first?

Man that's tough. Your motherboard is not even good enough to fully support your cpu and your video card is not meant for gaming.

You just about need an entirely new system if you want to game.

What psu do you have?

I will try to help you as much as possible. The first step should definitely be saving up some money, but that should go slightly faster if you sell your old components. You won't get much from selling older components, but it is a start. The first thing I would do is save up about 300 to 500 dollars at least. The rest is a bit tricky because new components get released all the time.

I would start with a new motherboard and CPU. To do this, decide what companies you will buy your CPU from. The two CPU companies are Intel (Haswell / Broadwell, Skylake, Kaby Lake) and AMD (nothing good from the past, Zen). For your budget, AMD seems like the better choice if the historical price range of AMD stays true for the new Zen CPU. I personally prefer Intel to AMD because of Intel's obvious higher performance in the past, but AMD usually has much better prices showed by their GPUs. If this trend continues to be true, a full AMD desktop might be a good choice. If you decide to go AMD for a CPU, get the just announced AM4 motherboard when the prices go down. Waiting for prices go down should give you enough time to save up. Then, get a low-end Zen CPU that should also have fallen in price by that time. If the Zen prices defy AMD's low price range, do not despair. Intel still has quite a good low end CPU market with their i3s and Celerons being quite good. This would mean you would get a 1151 motherboard instead of an AM4. Don't forget you would need a CPU Cooler like the Cryorig H7 or Cooler Master 212 EVO.

The next step is getting a new GPU. Some people might argue that getting a new GPU is more important first, and it can be true, but the motherboard is so bad that I don't think a new GPU could even be used at its full power with it. And if you get a new motherboard, a new CPU has to, most likely, come along with it because of compatibility issues. AMD is definitely what I would go for for a lower priced CPU. The rX 460 and 470 are your best choices. I recommend you get the rx 470 but the 460 is not too bad if you really need to go at a low price in exchange for lower settings. The GTX 1060 > rx 480, so I do not recommend you get the 480. My recommendation would to either get the rx 460, 470, or the GTX 1060.

There may be other things that need updating that I can't recommend unless you give me your whole build, but here are my recommendation on the RAM. This is the last thing you need upgrading. The DDR4 ram really doesn't give much of an improvement over the DDR3, but you may need to get DDR4 if the AM4 motherboard you get does not support DDR3 RAM. PSU definitely needs improvement. 500W or 550W is probably the sweet spot right now for PSUs. It is high enough to do be used for any non-SLI graphic card set-up with a great price while still being future-proof. I really like EVGA SuperNOVA 550w G2. DO NOT BE CHEAP ON YOUR PSU. A bad PSU is the only part that can damage your whole computer. Do not fall for that mistake. I would honestly rather get a rx 460 and a good PSU than an rx 470 and a mediocre PSU.

I hope this helped

Agreed, with that current build upgrade ability is very limited, and any investment would likely be a poor choice.
Keep that as a regular basic workstation build and save up something like 600-700 for a good 1080p 60fps gaming PC.