You're right that you can apply from within Germany. You'll need your passport, valid
health insurance, apartment contract, local registration from the Rathaus, enrollment documents (or the official letter accepting your application if you haven't yet formally enrolled) and the docs showing your financial support. It costs about €60 or so for the visa. I got my visa the same day I applied - took about an 1 1/2 including waiting. But I also live in a small town, not the Munich KVR.
If you are under 32 you have to have health insurance. If you are getting the German state insurance (not cheapest but least hassle), then you'll need a German bank account. You can get the insurance before official enrollment if you have a letter admitting you into the course. You'll also need the German bank account if you are going to live in a student dorm. Otherwise you might get by with a foreign account if you wanted. To get the local registration from the Rathaus (anmeldung) you have to show your apartment or room contract.
When I was helping some students with this last year, the auslanderamt told me that the student should have at least the rent + €500 each month coming into the bank account. It really does depend on who you get at the Auslanderamt though!
PM me if you want more info.