I'm probably too late to this but I am a restoration specialist. I'm the guy that makes the natural disaster/fire look like it never happened. So here's what matters:

1. Popcorn ceiling absorbs moisture. Water mist will remove it and so will latex paint since latex paint is water based. If you put latex over popcorn the popcorn can start to fall off or make a bald spot etc. If you are not planning to remove the popcorn then what you want to do is prime it first with an oil based stain block primer (SW has a good one that I use).
2. The stainblock primer will stop any nicotine or grease spots etc from weeping back through. If you skip straight to latex, nicotine is oily and will bunch up and make orange blobs in your finished product. BUT, primers also absorb. If you only use primer the ceiling will yellow with age and pick up dirt faster. So you need both.
3. Cover the stainblock primer with the flat paint they already sold you (this is the right product for ceiling). Both primer and paint can be rolled on with a 15mm roller just fine, just do one coat front to back and another coat side to side of each product so that you dont have missed spots.
4. The popcorn ceiling will look great for many more years and can be washed with a cloth or repainted for maintenance...but it won't be easily removable with water anymore.
5. If you have bare patches of popcorn DO NOT buy the spray can popcorn from the local hardware. It will not look good I can almost guarantee it, just going to make a mess.
6. If you are kinda handy and want to give it a shot, spraying popcorn is actually kinda easy because if it doesn't look how you want you can scrape it off in 10s with a wide trowel and try again. Equipment is rentable. There are 3-4 main types of ceiling texture, take a picture of your ceiling then do down to the place that sells it and compare your ceiling to the samples. Once you have the correct texture then spraying it just becomes a game of getting the ratio of water content, nozzle size, and air pressure correct. So spray at a blank wall and start dry, spray high and low pressure. Then add water, spray at high and low pressure. Eventually it will look close enough, apply to ceiling.

Good luck DIYers.