If you satisfied with the condition of the drywall after you remove the wallpaper as well as the quality of the drywall finish, sure, you can paint without having a texture.

Flat paint hides boo-boos better than semi-gloss/ glossy paint.

I'd steer away from adding any texture to the paint, especially in a kitchen. The only stuff I'm aware of is a sand texture. Had it in our family room until I textured over it and repainted. It is beastly stuff to wash & I like to clean my walls & ceiling every couple of years.

You can paint a wall that does not have texture, sure, but you need to have that wall in PERFECT condition. No bumps, lumps or holes. So the answer to your questions is another question....how do your walls look now?

And, one more thing...that texture stuff that goes in the paint....it's yucky and bad in a kitchen. It isn't washable (it will fall off as you wipe it down). I've used it...it was a huge mistake!

Smooth surfaces are MUCH easier to keep clean. You don't even want to know how gross the old popcorn ceiling in my "before" kitchen was! Walls in a any workroom should be easy to wipe down and sanitize and the kitchen is the biggest workroom in any home. Of course, smooth walls require more work on the front end so that the maintainence down the road can be easier. But, that's everything on the planet. It all comes down to 90% proper prep work and 10% "fluffing".

The renters we had in the home we're remodeling had TRASHED everything, including the interior walls. We (DH) had to spray texture or else we would have had to skim coat the entire house or re-sheetrock the entire house. It's not my favorite as I prefer a perfect smooth wall but those are hard to come by in an older home and harder to keep perfect. He used a light texture. I've added sand before to cover walls of a bathroom that I had to remove floor to ceilng mylar wallpaper from. It was necessary to cover the wreck that was left. The sprayed texture looks much better. Keep in mind... that I was on my own when I did the bathroom painting and my DH is a very handy guy so I don't know if the bathroom painting would have looked better had he been in the picture and done the work.

We have no texture anywhere in our house. Can't stand the stuff. You will have to be careful that your walls are perfect or each little imperfection in the sheetrock joints will show. It's not hard, just takes time and a good skim coat.

The '70s are over. Don't texture!

Not to mention ... you'll be back on the board 6 months from now crying ... "DH knocked a hole in the wall and we had to patch. How do I match the texture?"

It's also a dirt trap.

Go smooth. You won't notice tiny imperfections. Why pay extra anyway?

People still texturing?

As growlery said - 70s are over...

Go smooth, for a classic, clean, contemporary finish.

Thank you everyone, for responding.
After reading all of your comments, looking at our walls carefully and assessing the situation, we have decided to try to make our walls as perfect as possible, and then take the steps needed to paint over clean smooth walls.
Thank you again. You guys (and gals) are really awesome. I am so glad I stumbled onto this site a few months ago!
Denise

Denise, get a pole sander with a rotating head. Simple to use and the screens do a great job. After removing the wallpaper, be sure to look for any tears or wrinkles in the paper covering of the sheetrock. If you have places where the sheetrock was damaged you'll need to use some Zinsser Gardz to seal down the paper or the edges will bubble up under the paint.

Glad you decided against texture in the paint. Nasty on stockings, elbows and children of all sizes. Can't be wiped. Had it in a bathroom and HATED it. Tore the entire BR out last year and I'm a happy bather now.