If your SharePoint page has search results web parts already on it (like Core Results, Refinements Panel, etc., all out of the box stuff), you can trigger a search by just visiting the page and using the querystring
k=<your search query>.
So, you can create a standard Visual Web Part in Visual studio with the controls you need on it, and the button to start the search can just go to the current page and append on
k= in the querystring, and include your search. You'll need to append other search parameters into the querystring as per your selections in your other controls. So taking your Award example above, you could do a query in the text box that would append the following to the querystring:
?k=Some Search AND 'Award Notice'
If the data you want to search is stored in SQL, you will need to surface it in SharePoint via External Content Types first, so that SharePoint Search can crawl and index it. Here's an article on MSDN on how to do exactly this: http://msdn.microsoft.com/en-us/library/ee557243(v=office.14).aspx