If you have a solid color to select and delete, which the tool is the quickest and most effective?

The Magic Wand is the most ideal tool since the area of selection in question is solid. 

Magic wand is the quickest tool to use

Magic Wand tool or Marqee tool

the fastest way is the magic wand tool.

Use Magic Wand tool (W) then press tab to erase selected solid color.  

Magic wand tools with 20% tolerance

Use the magic wand tool with a 0% tollerance

Majic wand If  it's a 

solid color

Among of tools which are quickest and most effective for select and delete solid color Eyedroper is the best tool

 

Most easy is the Quick Selection Tool (W). 

You can use more than one tool, depending on what the software you're using. In photoshop you can select that solid color with magic tool then delete it. But if you use adobe illustrator you will need to make a shape and paint it with same background color then emerge your shape with that background to get empty background.