It's fine to use the bank for your lender. You will still have all the rights and protections that come along with any home purchase. You don't need to worry too much about the title search because that will be performed by a third party title company anyway.
Banks make money by lending money, so there is a good chance they will offer you a better deal because they have the opportunity to make back some of their loses by lending you the money and collecting interest over time.
Just make sure you have a good real estate attorney involved in your purchase so they can look out for your best interests. If at all possible, have your attorney try to get the bank to transfer ownership to you with a special warranty deed instead of a quit claim deed.