Best core workout?
I don't know whether there is anything 'best', it always depends on yourself, what you like, what you are capable of aso.
I personally like e.g. the Plankster Challenge
Swiss ball pike to jackknife
Core or abs? Anything requiring the core to stabilize the body for long periods is key for core strength. If you wanna pop those abs out fast get on a good diet and do dragon flags... they'll be washboard material in crazy time. Warning they are very hard on your body if you're not strong.