Realtors have the means to professionally guide you in your purchasing process. They can use comparable homes on the market, and they can use their knowledge of the area from their years of experience in real estate.
If an appraisal is done on the property a lender will use this number to base their financing of the property. Unfortunately this is not usually done until after the offer has been submitted.
Remember you are a part of a larger group of buyers, you are what we call the Market. The Market determines what price they are willing to pay for a home. This is why the same home can be worth 150,000 one year and a few years later could be worth 180,000.
It is what you are willing to pay after reviewing all the information at your disposal. Therefore it is Emotional.
You should have your agent give you information on what similar houses in the community have sold for in the last six months. Armed with this information you should make an offer for the house.
If you are getting a mortgage, the bank will get an appraisal for the property. If the appraisal comes in less than the offer you made, you should have your agent go back to the seller's agent and tell them you will not pay more than the house is appraised for. At this point there would be a new set of negotiations regarding the offer you made. Basically, the bank will not let you get a mortgage for more than the value of the property.
Wishing you all the best in your house hunt and purchase.