Airport/Weather (Buenos Aires)

Hello guys,
I will visit Buenos Aires from may 30th to june 4th and I would like to hear an advice how to come safe and cheap (if that combo is possible) from airport EZE to city center (I have no luggage and am fairly good with spanish).
And also, what kind of weather is expected, I suppose I should have a jacket/coat ?
Thank you all.

Have a nice evening!