It depends on whether you are renting or buying and whether you are living inside Israel or outside Israel. Outside Israel, if you are renting you are not required to put up Mezuzahs until 30 days have passed.

This is because only then is it considered a permanent dwelling. There are those who have the custom to put up Mezuzahs right away without a Brachah and then on day 29  take one down and replace with a nicer Mezuzah or just have it checked so on day 30 you can put up with a Brochah and have in mind the rest of the Mezuzahs.

​ If you purchase a home it is a permanent dwelling and therefore you are required to put up Mezuzahs right away I.e. the first night you sleep there, with a Brochah, there is no 30 day grace period. In the event you are slowly moving and using it as a storage house in the meantime there are opinions who hold you would need to put up even before you move in, ask your local Rabbi. If you are living inside Israel whether you are buying or renting you need to put up Mezuzahs the first night you move in.