The Invoice starter solution will work without any changes. You could make the fields more descriptive for your needs, but there is no need to change any relationship. You didn't state anything about contracts, you have a table / table occurance of contracts, but no other information. I would have to have more information on the contracts before I could give any recommendation about tracking that information.
If you use the Invoice starter solution. You would have multipe trips entered into the producst table which you could add contract inforation in the description of the trip.
You would then add a new customer or use an existing customer then add an invoice or modify an old invoice and then select the trip from the products table to enter on the invoice.