Residency for "other purposes" (Budapest)

HI everyone - day 2 in Budapest and the fridge is finally stocked, now I have to deal with visa issues so I don't have to leave after 90 days!

In Turkey where I've just come from, residency was basically a matter of showing up with the fee and proof of enough money to support yourself without working.

Being EU I expect the process to be a bit more difficult but I wondered if anyone has obtained a residence visa on the basis of being self supporting and has some advice or can direct me to any company that assists/advises in this area

Thanks! Virginia