Not sure if theres going to be a way to give a solid upgrade to all three of those with that budget. Getting a newer ddr4 board would require a RAM upgrade as well which isn't really cost efficient these days.

I'd say keep saving the money, and in the future put your money towards a new board, ddr4, and a matching CPU to go with it. Otherwise with that budget and motherboard you'll be stuck buying another 1150 processor which isn't an upgrade as much as a bandaid.

In the future do motherboard -> memory -> CPU -> Graphics card, I know this doesn't seem like the best way to upgrade your PC for games but it's kind of the hole you're dug into.

Edit: Looking into it, add another $40 or so to your budget and you could get the Memory, CPU, Motherboard issue sorted and keep using your GPU until you save more money for a used option or prices settle down. Something like this? [ Register or Signin to view external links. ] . I'm sure someone here can get you more for your money, I'm not much into builds anymore but this is just an example of what you could do.

I recommend a upgrading to a cheap Ryzen 1600 build or just upgrading your graphics card. You can get the CPU, Motherboard, and RAM for about $330 before tax and shipping. You can get the graphics card for about $360 if you live in a state where Newegg does not charge tax. You should see a good performance increase with either upgrade. Unless you do as Scizor suggested above and save up for a better build.

If I was personally in your position I would upgrade my graphics card to a GTX 1060 and a new PSU (your current one seems like a hazard) now and later on go for a Ryzen build when you get a bit more money.
Here is the Ryzen build I would suggest getting. [ Register or Signin to view external links. ]
Here is the graphics card I would go for right now. [ Register or Signin to view external links. ]

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You can buy a 4670k and R9 280x for $320 right here. $200 is over-priced for a 280x tho, so don't, just an example. Your best bet is going to be buying a used Haswell i5 or i7 as a a CPU upgrade, or stick with the i3 for now. Right now is not a great time to be buying in to a new socket, especially if you're on LGA1150. A used i5-4440/4460 should set you back $100-120, or $160-180 for an i7-4770/4790.

For GPU, $350 is waaayyy over-priced for a GTX 1060, don't do that to yourself. Buy a used GTX 970 or 980. Don't pay more than $200 for a 970, but you should be able to get them for under $200 easily. They were selling consistently for $150-170, but I've not seen many recently. For a GTX 980, $250 would be the absolute limit, but you shouldn't have too much trouble finding one for $190-220.