Most of the newer folding attic stairs on the market today are lots better than the rickety models installed in tract houses in the 1960s and 70s. In the case of these products, you get what you pay for; more expensive models are better made and generally have a higher weight capacity.
Putting temporary cleats across the stair's jamb makes it easy to hold it in place while you shim it. And while you may be tempted to nail the jambs to the framing, don't; use lag bolts instead. The little extra time and cost it requires will give you and your homeowner peace of mind.
If you're at all unsure of how to cut the bottom section to length, watch that part of the video a couple of times. If you cut the section too short the stairs will not reach the floor and will tend to bounce when climbed. And if you cut the bottom section too long, the stairs will not unfold all the way.
Finally, folding attic stairs can be a huge energy suck in a house. It pays to invest in an insulated hatch cover. You can either make one from rigid foam board, or buy a premade from Battic Door.