What about RAM? Old system using DDR3? Old system AMD or Intel?
Might lean towards a Pentium G3258 and a Z97 board so you have a better upgrade path. But that is easily doable.
AMD FX-6300 and a 970 chipset motherboard would be a place to start with that budget.
If you have an OEM copy of Windows, yes. If you have a Retail Box copy you can install it on a single machine at a time three times, usually requires re-activation by phone.
Swapping motherboards while re-using a pre-installed OS can sometimes be difficult. Though Windows is pretty good at loading new drivers for new hardware.