This one is admittedly not very well phrased.
From PHB1, p157-158:
Staff of Defense: A staff of defense grants you a +1 bonus to AC. In addition, once per encounter as an immediate interrupt, you gain a bonus to defense against one attack equal to your Constitution modifier. ... You must wield your staff to benefit from these features. ...
No, you do not automatically gain an implement, no matter which Implement Mastery option you choose.
Yes, any staff works, even a plain non-magical one (which is probably what you'll have at level 1).
Basically, as long as you're wielding a staff implement, any staff implement, you get +1 AC and can use the interrupt power it describes once per encounter.
From PHB1, p221:
Arcane Implements: ... A staff implement can also function as a quarterstaff.
Quarterstaves & staff implements are a little odd. Staff implements can definitely be used as quarterstaff weapons, per the rules; this implies that quarterstaves can be used as staff implements, and most groups play that way, but it's never actually officially stated in the rules.
Note, however, that regardless of how you choose to interpret that part it takes one hand to wield a staff implement (or any implement other than a holy symbol or ki focus) but two hands to wield a quarterstaff. If you have a staff implement in one hand and anything else in your other hand, you can't use the staff implement as a quarterstaff. If you're holding it with both hands you can use it as a weapon or as an implement, but if you're only holding it with one hand then you can only use it as an implement. Remember, every power will have either the weapon keyword, letting you know it needs to work with a weapon, the implement keyword, which lets you know it can work through an implement (though it doesn't have to), or neither of those keywords, which means it doesn't care what you're wielding.
No, wielding a quarterstaff will not prevent you from making ranged attacks. Well, it will prevent you from making ranged weapon attacks (unless you put it away and draw a ranged weapon), but as a wizard all of your powers (other than your melee & ranged basic attacks) should be implement attacks, which don't care what kind of weapon you're wielding.