Some Z87 motherboards will run haswell refresh and devils canyon, but probably need a bios update.
Broadwell... no. No telling which will or won't now.
Best to wait a week for a Z97 motherboard. And perhaps enhanced haswell chips.
It is supposed to work with current chips and future broadwell.
They cost no more and have better capability than Z87.
Past that, you will be fine with i5-4670K for gaming.
If beginning of June is your build timeframe, look for a i5-4690K(aka devil's canyon) which should cost no more and give superior overclocking.
Broadwell desktop is next year and will not be a compelling upgrade if you have a i5-4670K.