Everyone spends $$ to take the texture off the ceiling. Why bother to install texture. BTW, read the directions on your product. It will tell you how long it takes to dry thoroughly. Also, you will have to apply primer over the texture before you paint. Use a ceiling paint in a flat finish.

What has been said^. The old popcorn texture hasn't been cleaned off enough to skim. When I removed popcorn, I used hot water in a garden sprayer w/ some dish soap added. Sprayed, let it sit a bit and then peeled the texture off with a wide blade drywall knife. Then I did a skip trowel texture. If you want to try skimcoating it yourself, I would buy a drywall squeegee. I haven't used this tool but did use a plain old window squeegee on a problem area of drywall. Worked good enough for me to make a note to buy the drywall version the next time I have a need. (I suck at knife work; the squeegee felt much more 'natural' to me.) If you're concerned about water absorption that Live Wire mentioned. you can prime the drywall w/ primer or paint with a flat paint before skimcoating. Flat paint only because it's toothier. Don't use gloss, semi-gloss, etc.

My entryway

This is a controversial question and you can find it in the Houzz threads. Some people think it's cheap looking to paint the ceiling the same color as the walls. Some people think you should paint the ceiling, considered a 5th wall, lighter than your walls and in matte/flat so as not to reflect a lot of light. Some people are adamant the only color you should have on your ceiling is white. Bottom line: it's all up to you. I painted my Fort Worth home entirely in SW Softer Tan. I chose an eggshell sheen for the wall and flat on the ceiling, all the same color. I felt that the way the sun hit my primary living spaces in the afternoon made it feel like a warm cozy space. I hate the juxtaposition between a painted wall and a white ceiling. I'm in a rental right now and it confirms how much I hate white ceilings. And if you don't have a great painter you'll see the lines (if you don't have molding) and for me that's annoying. In the house I'm building, I have to get Bright White on the ceilings; it's annoying but it'll lose prominence with good decor and in a couple years when I'm ready to paint again that ceiling will be painted.