Ok, so a few things to note. WSS 3.0 is free software, so you don't need licenses for it, but you would still need whatever licensing is best for the SQL server being used for SharePoint. As for your forms, they won't actually be going to the database the way you may normally expect. They would go to the SharePoint form library. Behind the scenes, all SharePoint data is stored in SQL content DB that is part of the SharePoint farm, but it's not a DB you directly interact with. It is possible to create your own separate DB with tables that you build to either retrieve or submit data from your form to the DB, but that's a completely different beast than just submitting your forms to SharePoint.
So, did you intend on building a complete database structure for your timesheet data in SQL and then plan to interact with that data directly or through a web service from an Infopath form? Or, did you just mean you were going to have it published to SharePoint and users would go to SharePoint to fill out and submit forms with the data residing in SharePoint (within the forms themselves but visible as columns in the library)?
As for someone the comment that "someone was able to setup WSS 3.0 2 weeks ago," be very careful with this, because if it was just someone tossing it up without architecting it or planning for usage, scalability, security (and all that jazz), then be careful about building a solution that people would potentially use for production purposes . If you are just building a prototype as a proof of concept, then great! Just don't build it with the intention of employees using it for real unless you know the system was architected for production, long-term use. WSS 3.0 is free and is very limited, so you wouldn't want to go too far down the rabbit hole without knowing what's on the other side.