Welcome to the world of InfoPath :)
Default DB functionality will not accept large file types like the signature.
You need a web server and then you can setup a submit data connection, create a naming convention form the form data, and each form will be uniquely named as you want. Contractor company-name-timestamp or something.
You have kind of two options.
Setup a simple web server if you do not have SharePoint to submit forms to.
The drawback is when they are all individual xml files you cannot do reporting and analysis of the data.
If you like InfoPath and have other areas you could use electronic forms, such as help desk requests, HR forms, plant documentation etc. Then I would recommend a little investment in your backend resources so that you could really have a great foundation to build upon.
I would look at putting a SQL database in, if you do not already, and purchasing an installable package of webservices. (www.qdabra.com). This will give you the ability to database all of your data, even large file types, and be able to report via web reports or Excel on the data. It also includes Active Directory integration for identifying the form user or their manager for workflow, and the ability to query data from databases. This is perfect for an admin like you since it also does not require code or complexity. You can be a hero pretty easily.