I'll go with the second option. Save a little and invest the rest. I believe that is the wisest thing to do. It would be so bad if you had little money, at least in savings, so that if anything had to go wrong in the future, you would stretch your hands in there and settle the problem without having to risk your investment. Investments are for financial elevation, which is why it is essential to invest. Both investment and savings are necessary, which is why it is important not to put all eggs in one basket, they should be done alongside each other.
It is a very big mistake if a person uses all their savings for investment purposes because as you said, savings are not supposed to be used for investments because emergencies can come at any point in life, and when that happens, one would need funds for the emergencies, and in such situations, one wouldn't be able to withdraw their funds from the investments they've made which is why it is important to have savings.
If one can afford this, they should have two funds, one should be their savings and the other should be for investment purposes, so that when they invest their investment funds, they would still have their savings intact and in emergencies, they can use those savings.