You want to jack up front to rear (or vice versa) and support it in kind. Do not jack it left to right.
You're good on the jack placiing. Placing the stands under the rails is also correct. The pinch weldes on the body area tend to fold under the weight.
After I put a car on stands, I typically give it a good nudge or 3 to feel any wobble while it's up. If it feels unsteady, it probably is.