The description of the Spiritual Weapon spell says:
... When you cast the spell, you can make a melee spell attack against a creature within 5 feet of the weapon. ...
Does it mean I can attack with Spiritual Weapon with my action only in that case?
If it doesn't, then does it mean I can make 2 attacks with Spiritual Weapon using my action and bonus action next turn?
... As a bonus action on your turn, you can move the weapon up to 20 feet and repeat the attack against a creature within 5 feet of it. ...
Does it mean I should choose only 1 target for Spiritual Weapon?
Contrary to what you imply in the question, spiritual weapon takes a bonus action to cast (PHB 278), and thus you cannot attack with it as an Action even at the time of casting. About the later attacks we read that:
As a bonus action on your turn, you can move the weapon up to 20 feet and repeat the attack against a creature within 5 feet of it
The spell does not grant you the option to use your action, only your bonus action. Since you have only 1 bonus action in a round, you can only attack once and only one target ("attack against a creature" = 1 creature).
However, there is no indication that you have to attack the same creature every time, so you can choose each time you attack.