In that price range, you might be able to get a Radeon RX460. Otherwise, a GTX 750Ti or GTX 950 are good choices.
Motherboard choice doesn't matter much. Pick one with the slots you want. As long as it's from a good brand (Asus, ASRock, MSI, Gigabyte), more expensive boards will not have any impact on performance or stability, they'll just have more connections and ports on them.