Another variation is to make the frame out of 2x4, hang the hatch/door
on it, then fit the whole thing to the surrounding joists. This is a
good option if you're fitting a ready made insulating loft hatch set.

I'd always do it that way. Fitting a door to an existing frame that is
unlikely to be perfectly square can be a pain IME

Melamine coated chipboard makes a good general purpose loft hatch, as
long as you have the equipment to cut it clean& square.

No good if you're fixing hinges to the edge though. Blockboard or
"pineboard" is lighter and will take a size 6 screw