Fixed Price or Time and Materials?
Fixed Price Project
A Fixed Price Project is one where a software provider gives you a fixed price cost for an implementation and this is what they agree to charge you regardless of the actual time spent on performing tasks.
Generally this price should be based on a pre-defined Scope which covers the interests of the software provider as well as the customer. The Scope should define exactly what will be done for the price and anything that is not included in the scope is not considered part of the implementation. There are no assumptions.
During the implementation there may be items that were overlooked and become requirements. Your software provider will draw up a change control document outlining the impact of the change on the scope, this could be time and or money.
Most people prefer a Fixed Price Project as it helps to know the cost up front and budget accordingly.
Time and Materials
A Time and Materials Project is exactly that and the software provider will charge you for every hour that is worked on your site. This sounds like it would always be more expensive but is not always the case.
There should still be a Scope drawn up as mentioned above so that you both know where you are headed, as well as a cost estimate. You should also still manage any variations with Change controls so that you are always aware of any impact on the budget.
Although these types of projects are not necessarily always more expensive there does need to be a certain level of trust between the Service Provider and the Customer for an agreement like this to be successful.