Mechanic's check
 

What should I ask the mechanic to do when I bring in the car - a basic diagnostic, lift up the car to look for welding on frame, ...? What are the specific phrases/things should I ask the mechanic to do?

You can say the following - I am considering purchasing this car and I want a careful and detailed inspection of the car's condition. And ask them what they will check and how much it costs. That should do it. Typically this is $75 -120 range.