Highest bidder...

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My wife and I recently made an offer on an REO that was 15% below the asking price of 230000. We were just informed that the bank was countering another offer and when our offer came in, the bank said that all interested should offer the highest amount and they will deal with them. I am new at this so I don't know what I can assume. If the bank was in counter offer/ offer mode with the other potential buyer, and then with our offer the decided to open it up, could this mean our initial offer was higher? Also, we are interested in the property for a permenant residence and we like the place but it does need some work, which we are willing to do but we don't want to pay thru the nose for it as this would likely diminish the decent deal we would be getting with an REO. We can afford full price, but definitely don't want to pay it. Can anyone with experience in these matters give advice on how much to offer? I am sorry to be asking such questions but I am new to this and the bank has given us until tomorrow to submit our offer. Thanks all.