Will the Core Set cards be avaliable for the Wild format?
I'm a wild hearthstone player and was just wondering if I could play the new Core Set cards in the Wild format when the new set goes live?
You can use the core set in Wild. Confirmed in Blizzard's announcement blog.
https://playhearthstone.com/en-gb/news/23620129
Is the Core Set only playable in Standard?
No. The Core set can be used in Wild as well.