It was too big to post as here, so converted it to a blog instead. Hope you find it useful.
I agree with John and Tina. Using the comps will help you determine the price you want to offer. However, in today's market, it all depends on how many people want to buy the same property.
First thing you want to do is go take a good look at the property then make the best offer you can within your budget. If you are using a real estate agent, he/she will be able to assist you in writing a competitive offer.
There are also other factors to consider when writing your offer. Offer price is only one piece of the puzzle. If you are not working with an agent which it sounds like you are not, I can help you with the offer price as well as the other pieces of the puzzle in this crazy market right now.
This is exactly why you should be working with an agent who can do this work for you and help you with these kinds of questions to put the best offer together for you and help you get the house. Feel free to contact if you need anything else. I wish you the best in your home search.
You need to be provided with a comparative market analysis so you can see what comparable homes in the area have sold for. You need to realize that it is likely that you will be in a multiple offer competition for this house. After you have been provided with the data in regard to recent sales you need to ask yourself "How badly do I want this house?" Based on your answer have your Realtor write up your offer.