LGA 1151 Upgrade Recommendations

[Apollo Serenus]

My i5-2400 has recently started to show it's age. My peaks and tweaks have reached the end of their limits.
My current setup of what I"m looking to upgrade is a HP 8200 Elite running a i5-2400 processor with 4x2GB DDR3 and Windows 10..
I'm looking to upgrade to a i5-6600k and I need motherboard suggestions. Since new RAM is not in the budget, I need to stick with my DDR3.

This PC is for gaming, browsing, and running Unreal Engine for developing the 16-bit style video game I'm working on.
I've never been a graphics elitist, so high end graphics for gaming are not needed. Lower mid-range is fine for me.
Also, having a weaker PC serves my needs for development perfectly because if it can run on my system, it will run on everything from next-gen down to budget mobile without issue. I don't want people complaining it doesn't run well for them and my response being, "Well it ran on my Binford 11,000 without a problem."

I've included a photo of a non-modified 8200 Elite. Mine has modifications to the rear framework to allow space for a non-small form factor graphics card to fit. (Tin snips are fun and will be used again if needed:)

Thanks for your time, thought, and responses!

HP_Compaq_8200_Elite_PC_-_i5-2500_3.3_4GB_500GB_DVD-RW_Win7_Pro_COA_-_2UA1401HFK_5_grande.webp

[Electronics Wizardy]

What is your total budget?

 

That looks like a micro btx case, so really, your not easily just swapping the board.

 

I wouldn't get that 6600k, not official support for ddr3, and why buy an old cpu, much better spending a bit more for the ddr4 and get a much better cpu and platform. 8gb of ddr4 isn't that much now.

 

You could also go with a i7 2600 if you can find them cheap, or get a newer used office pc.

[Fasauceome]

12 minutes ago, Apollo Serenus said:

I'm looking to upgrade to a i5-6600k

why this specifically?