Both potřebuji and potřebuju are grammatically correct. Like you said, "potřebuji" is used in formal texts, "potřebuju" is used pretty much everywhere else. You've made a little mistake there though. You need the accusative "pro ni" (short i).
Confirming. The difference between "ni" (short) and ní (long) can be very important. Try to think of a sentence "Myslím na ni. Making the same mistake (na ní) will change the meaning from "I think of her" to "I think on her." Very easy way to get slapped ;-)