Painting the popcorn is better than nothing, but if you're wanting to sell your house, many people don't like popcorn. It's not the in thing now and makes the house feel dated.
If your budget is small but you're willing to put in some sweat equity, I would suggest you consider removing the popcorn. I did it in all the bedrooms in my house plus a hallway. It is a little messy, but it's really not that hard. You'll likely have to do some patching, but if you're careful, you shouldn't have to do too much. Then a quick coat of paint and you're done.
I think it's fair to say that most people, if given a choice between painted ceilings and popcorn ceilings, would choose the paint. This may give you an edge in selling.
I agree that taking off the popcorn is the best way to improve things. If it has asbestos, then protect yourself when you scrape it off. Wear some disposable clothing if you want, but for sure, you need lung protection (a good face mask) and eye protection.
If you spritz the popcorn first in small sections to wet it, it comes off easier with less dust. When you get all the popcorn off, you will need to wash the ceiling down with water and a large sponge, changing your bucket water frequently. Gather up all plaster drop cloths with the debris, and dispose of it properly. This may mean at your county landfill - they will charge extra for asbestos.