The obvious upgrade is to a Z270 MAXIMUS IX or STRIX motherboard, along with i7-7700K and a dual-channel DDR4 kit.
Your existing CPU block/cooler might be compatible with LGA1151. Or it might require you purchase a socket-refit kit (which should be cheaper than replacing the entire cooler). Chances are LGA1151 wasn't around when you bought it, but if your block/cooler is still on market then the advertising will be updated with LGA1151 (in)compatibility.
To be honest, you'd gain almost as much general performance by upgrading your i7-4770K to an i7-4790K and your memory to a dual-channel 2x8GB DDR3-3100 kit (the best officially "supported" by your M6F mobo, although in reality you should expect maybe only up to DDR3-2133-ish or DDR3-2400-ish performances with a modestly-overclocked "average" CPU part).
The only "weak" hardware on your rig (in "dire need" of upgrading) is the two (230W) GTX770 cards, you'd get better gaming fps (and dramatically reduce power/heat) by replacing them both with a single (150W) GTX1070. Your M6F is a fine mobo, so there's actually no requirement to upgrade it, as long as it keeps working and you can still upgrade to top-spec LGA1150/DDR3 parts for it.
i7-4770K = 22nm LGA1150, 4C/8T, 3.50GHz~3.90GHz, 8MB, up to 32GB dual-channel DDR3-1600, 16xPCIe3, 5GTps DMI2, 84W (72.72C)
i7-4790K = 22nm LGA1150, 4C/8T, 4.00GHz~4.40GHz, 8MB, up to 32GB dual-channel DDR3-1600, 16xPCIe3, 5GTps DMI2, 88W (74.04C)
i7-6700K = 14nm LGA1151, 4C/8T, 4.00GHz~4.20GHz, 8MB, up to 64GB dual-channel DDR4-2133, 16xPCIe3, 8GTps DMI3, 91W (64C)
i7-7700K = 14nm LGA1151, 4C/8T, 4.20GHz~4.50GHz, 8MB, up to 64GB dual-channel DDR4-2400, 16xPCIe3, 8GTps DMI3, 91W (100C)
(looks a lot less impressive when you consider that most i7-4790K and i7-7700K parts overclock up to roughly the same 4.8GHz~5.0GHz)
(SKL and KBL have smaller lithography and higher TDPs ... where'd all the extra silicon go? ... into the useless fancy new iGPUs, lol, yay).
And don't forget about AM4/Ryzen!
Your i7-4770K is roughly equivalent to an R5-1500X, but many better
Ryzen CPUs are available, and Ryzens cost substantially less than their Intel counterparts. AM4 motherboards - all newer than your M6F - also generally cost less than their Intel counterparts, aside from extreme offerings like the ROG C6E.
I don't think this is a good time to buy GPU cards, though. AMD Vega and NVIDIA GTX 20 Series (and Volta) are just around the corner. And bitcoiners have apparently driven GPU demand (prices) up in recent months. The best NVIDIA GPU cards currently cost too much. The best AMD GPU cards aren't inflated as much but they also aren't as powerful; replacing your GTX770 cards with RX580 cards would be a "good" upgrade that costs as much as a "great" one.
If your rig still does whatever you do fast enough and well enough then upgrade it later, once more Ryzens and (upcoming) Coffeelakes (and upcoming GPUs) have started flooding the market.
If it's starting to slow you down or look ghetto then get new GPU card(s). (After bitcoin value declines and people start pulling out because so many people have gotten involved that per-capita "revenue" become negligible trying to hash on GPU-based hardwares.)
On the plus side, today's GPU cards consume less power than yesteryear's GPU cards. So it's unlikely you'll need to upgrade PSU.
On the down side, if your GPU cards are watercooled you'll need to factor in added cost of waterblocks (or hybrid/watercooled) cards.
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