Popcorn ceilings can be removed with a good old fashioned 6 in drywall / spackling knife. Granted it is messy and time consuming, but I have found it to yield the most consistent and reliable results.

If you are putting down hardwood floors, definitely do it in this order

1. Remove Carpeting
2. Repair and Paint Walls
3. Install Hardwood Floors

Now, if you are doing work on the ceiling, I would do that either just before or just after step 1.