I keep a scissor jack in the truck. You should avoid getting under a car without jack stands but if I have to, I feel more comfortable with a mechanical jack in place, rather than hydraulic.
As far as the height required, jack it up with your shop jack to the point that the tire is off the ground, and measure. You'll need a jack that will reach that height. It doesn't need to be heavy duty, either - you won't be lifting the whole car with it. Probably the lowest rating will be fine and that should keep it smaller and lighter.
Lawrenceville, GA