What document do I need to provide immigration for my Non O visa application after transferring funds to my bank account?

you need the "standard" bank letter ( usually about 5 or 6 lines that say your name your account number and the balance) AND you need the bank book updated showing that the funds came into the account from abroad (it'll be coded as an FTT usually on the bank book for that line item)

SO get the bank letter AND get the statement AND update your bank book on the day you go to the immigration office to apply for the 90 day non-O