You and the Seller Must Agree
Buying a home does not occur in a vacuum, involving only you and the seller. There are all kinds of people and services involved behind the scenes to make it happen. Since some of these services affect both you and the seller, there will have to be an agreement on which companies you will use for them. When you make your offer, you should request your favorites for these services. If you are unfamiliar with these service providers, you can get recommendations from your agent.
Title insurance is important because, by providing you with an Owners Policy, they insure that you have clear title to the property. If there are any problems later, you can always go back to the title insurance company and have them clear it up. Since it is customary for the seller to pay for the owner's policy, they have an interest in which company is used.
However, you are going to pay a fee to the title insurance company, too. This is for the Lender's Policy. The lender's policy insures your mortgage lender that there are no liens or judgments against the property and that the mortgage will be in first position. In other words, should you sell the property or refinance it, their mortgage gets paid first, before any other claims against the property.
The lender's policy is less expensive than the owner's policy.
Escrow and Settlement
For example, you are going to need an escrow or settlement company to act as an "independent third party" between you and the seller. Without having a third party involved, how do you know that when you fork over the money, you are going to get the deed? This is the type of service provided by escrow and settlement. They will hold your deposit and coordinate much of the activity that goes on during the escrow period.
Since this third party is very important to both you and the seller and both of you will pay fees to this company, it is important to agree on which service to use. Therefore, your choice should be part of the offer. Since you do not buy a home every other week or so, you are probably unfamiliar with companies that provide this service. Your agent will make a recommendation. You have the authority to accept this recommendation and include it in your offer, or make your own choice.
Keep in mind that the seller will also have a preference and this may be a point of negotiation in a counter-offer. It has become customary that one side will choose the escrow/settlement agent and one side chooses the title insurance company. Even so, everything in real estate is negotiable.