Don't expect the bank to jump at your initial offer. They will probable counter your offer with a number somewhere between their asking price and your offer.
Banks don't like contingencies and will more than likely veto this part of your offer. They do like paying a portion of the closing costs and using their closing company for the transaction. This will provide them with greater security and control of the closing process....It seems their philosophy is "too many cooks spoil the broth."
Since I'm not in your area, I can't say for certain what will come of your offer, but I'll offer what I have noticed in my area (NW Ohio). First, banks are very overwhelmed with properties and offers right now, so your response time from them will very possibly be a few weeks or more. Another reason for banks to take their time is that a second or third offer may come in the meantime, leading to negotiating power for them. Second, banks have been very open to covering closing costs, so I think that you are likely fine with that. Third, it's hard to say whether the actual offer amount will be taken or not without knowing some specifics, such as condition of the property, what market values of homes in that particular neighborhood are, what the list price of the home is, etc. For example, if the list price is $200,000 and the home is in good shape, and the average for the neighborhood is $300,000, you're already getting a pretty good bargain at the list price, so getting it for $174,000 plus closing costs might be a little low. However, if the house is in poor condition, or if the bank just needs to get rid of its inventory, your offer might be a good one. Strictly based on your information, I think that you shouldn't be too concerned over your offer, it seems to be pretty reasonable. Just sit back and wait for the bank's response. Good luck in your purchase!