Usually you need to prepare 4-6 month of monthly rent for the initial costs of renting a place. Monthly rent is the rent itself + management fee.
Initial costs to rent a place
Management fee. The money to maintain your place.
Rent. Usually they take the month you moved in (前家賃、当月分), depends on how many days in the first month (日割家賃), and the next month rent in advance (翌月分の家賃).
Deposit (0 ~ 3 month)
Usually is about 1 month. This is used to restore the room into original state when you finished the contract. The money left after cleaning will return to you.
Gift money (0 ~ 3 month)
Fire insurance. ¥10000 - ¥30000.
Gurantor company fee.
Fee for agent. 0-1 month.
Money to clean the place you will move in.
Key money. Usually ¥10000-¥25000.
Money to make new keys for the place you will move in.
Besides these, you will also need to prepare 引越し費用. Hiring company to move all your belongs from old place to new place. If this is your first time in Japan, you will need to buy furnitures and appliances (washer, bed, curtain).
I have heard of but they are not common.
The money needs to pay after contract signed
A money to reserve the property; Rare
Omiyage for your neighbors.