What year is the house. You say older… for some folks that means 1990’s… for other folks that’s 1930’s…
Popcorn ceilings may or may not have asbestos – and you need to properly dispose of it (not the dump) if it does have asbestos… You can buy a kit to test it (you send it off to a lab) at Home Depot.
If it does have asbestos – you need to hire a contractor – unfortunately… Regular joe-schmoes aren’t allowed to dispose of asbestos material.
Removing the popcorn ceiling can be a DIY job. We did it in our house (for the non-asbestos portions… our house was 1/2 and 1/2 due to a burst upstairs pipe causing the downstairs ceiling to be replaced in the 80’s.) It’s kind of like removing wallpaper… get it wet – scrape it off… messy but not really a skilled labor type of job. Texturing or skim coating the ceiling is something you might want to hire out.
I disagree with the comments that you don’t have to spend as much time if a GC is running things. It’s still up to the owner to make sure the project stays on track, and is done correctly. Maybe it’s just our bad luck – but we had two GC’s and in both cases, supervision of the subs was non-existant.