I have build a few Internet Facing Sites. Most of them have been on SharePoint Server variations , which require you to have Internet facing License along with a few restrictions on the usage of that farm. For eg: I believe an Internet Facing Farm / Web Application cannot be used to serve "Internal" consumption of the farm.
The reason some companies go for the paid version of SharePoint against Foundation is to utilize on service applications being spread across multiple servers, publishing features , page layout issues etc.
When taking Foundation into the mixture , you need to get an Internet Connector license ( I may have got the exact name) but that is for your Windows 2008 R2 / 2008 box to be placed in an Internet facing scenario. I believe you only need your Web Front Ends to be licensed in that case as you wouldnt be exposing your APP server to the Web.
About SQL - Not the strongest believer of Express , but if you are expecting less than 300 users or so a month to your site , I think Express would be the right choice of SQL for you.
If however you are going to be standing up a high volume of Internet users recommend either look at hanging off your existing SQL infrastructure or build a new one for this farm.
This link here shows a bunch of SPF2010 Internet facing sites - http://www.wssdemo.com/livepivot/#/viewerStateKey/62d7ec5d-e5b0-46ae-873d-f46e82ae7417