Typically, the party that will be providing the services will sign the contract first. However, it doesn't particularly matter the order in which the contract is signed, unless amendments, or changes, are made to the agreement. Amendments to a contract are usually made before anyone has signed it. You may want to inform the other party of any changes you wish to make, and make sure the changes are made to the contract before signing it. If changes need to be made to a contract that has already been signed, you might consider using a Contract Amendment to make the changes official.