Adding a 'wave/ripple' effect to a moving sheet of paper ..?

Well I don't know if realism or "life" are the things it lacking.  Paper isn't alive & for intents and purposes it already looks like a piece of paper.  The problem is that the animation is boring.  This can be fixed using other elements and basic animation principles.

I don't think there's much you do to the paper itself.  maybe use page turn effect to give one of the corners a little curl?

Have it rotated a bit off absolutely straight

I think it could slide in a little faster.  I feel like between 15 and 20 frames is the sweet spot.

Secondary motion:  like bounce or overshoot.  Or Attach the paper to a null and scale the null up slowly starting at the papers first position keframe and finishing way past where the slide in stops so the paper contiues to scale up slowly after it slides into place.  You could add a little rotation in the same way, to the same null.

Secondary elements:  give a background.  Maybe it's being held by a hand or sitting on music stand.  Maybe put a blurred out image of somehting musical or something abstract like floaty music notes or staffs.  You could have the background slide in few frames before the paper to create some anticipation and or offset.  The background can also have secondary movement slightly offset from the papers

Basically....add interest.  Don't let the screen just go static keep some very subtle motion or movement going all the time.

Try applying the Page Turn or CC Twister effects.  The key is subtlety with these, just a little bit of flutter on the corners can be convincing, go overboard and it just looks silly.

If you want to get more elaborate, you can look at third party 3D deformation plugins, or Cinema 4D, but I'd stick with the basics for now if you're new to After Effects.