The basic account for day to day use is a "Savings Account". This offers very low interest but deposits and withdrawals can be made without limitation. Alongside this account you can open a "Fixed Deposit Account" which offers a higher interest rate based on keeping the principal amount in place for the agreed period. Withdrawals can be made but interest will then be reduced to the very low Savings Account rate. The 800k you move in should go into whichever account you are going to show at immigration in order that it is clearly seen as a foreign transaction. They main thing for immigration is that the funds are immediately available to you.
To open an account you should be OK with your non-O visa. I was also recently asked for a copy of my apartment rental contract in order to open a new account. Your experience will vary depending on many things; bank, branch, staff member, phase of moon, etc. The main banks websites are pretty clear and give all the information needed about their products.