Which webpart to use to add, delete, update data from a database table.

what you are looking for is business connectivity services. now I am not sure if this existed with the same functionality in 2007.

http://pravahaminfo.blogspot.be/2011/06/business-connectivity-services-bcs-in.html

No not that i know of! any way that you chose you would need to create some code! there are alot of examples out there on the net!

For your issue it shouldnt be hard atall! just create three stored procedures for each task in SQL server, make sure you give each stored procedure the correct permission.

create your custome webpart and call the stored procedures from there!

somthing similar to this ;)

http://www.codeproject.com/Articles/33862/Connecting-to-Database-Using-Custom-Webpart-in-Sha

you can follow luis route:

Creating a Database Connection by Using the Business Data Catalog Definition Editor

http://msdn.microsoft.com/en-us/library/bb736296(v=office.12).aspx

EDIT

for sql commands

http://msdn.microsoft.com/en-GB/library/system.data.sqlclient.sqldataadapter.insertcommand.aspx

to add buttons to webpart:

in create child controls even add:

protected override void CreateChildControls()
{
   //create a new button object
   Button btngo = new Button();
   //give the button some text to show
   btngo.Text = "GO";
   //create the button click event
   btngo.Click +=new EventHandler(btngo_Click);

   //add button to control list to display
   this.Controls.Add(btngo);
}

//do what you want in the click event for the button
private void btngo_Click(object sender,EventArgs e)
{            
     //do what you want here on button click ;)       
}

I suggest you to use BDC (Business Data Catalog) in Sharepoint 2007. BCS is an upgraded version of BDC in Sharepoint 2010. So since you are using 2007, you should look for BDC.

You can use the BDC Web Parts to View, Update, Create, Delete items to the database.

Here is a tutorial to get you started:

http://zimmergren.net/technical/sharepoint-bdc-part-1-getting-started-with-the-business-data-catalog