It's worth noting that Intel's 6th generation CPUs do not support DDR3, only DDR4 or DDR3L. The problem with DDR3 and Skylake is that normal DDR3 runs at a higher voltage and it's commonly believed you may damage the memory controller over time by running high voltage RAM, but I haven't seen evidence either way. You might want to do some reading on this.
You could try using your existing RAM in a board that supports DDR3L, or you could sell it in the classifieds and move up to DDR4. They cost about the same so the upgrade probably wouldn't cost you much, but sometimes every dollar counts.
What I typically do is get on PCPartPicker and look for the cheapest board available that has 4 DDR4 slots (if it's not an ITX build). After that, I might rule some out that lack something specifically I want, like a second LAN port or M.2 slot. Right now there's an Asus B150 board with 4 DDR3/L slots on sale on Newegg for $38 after rebate, but typically you're going to be around $55-60 for basic boards. More expensive boards are not necessarily better, they just tend to have more "stuff". Stick with Asus, MSI, ASRock or Gigabyte and you'll be fine. That's not to say other manufacturers may not make good boards, and I went with Zotac in the PC in my signature because it offered what I wanted, but YMMV.