Specific Counter Setup: Add Amount per Frame Until Value is Reached

You can use sourceRectAtTime() to find the height and width of any layer. As long as the anchor point for that layer, or the Transform Shape/Position and Anchor Point, are at zero, the following expression will move any layer from the left edge of the frame to the center of the comp in 20 frames. If you want to change the move speed, change the * 20 to another value in the tMax variable. It works with any Text layer, shape layer, solid, or footage of any size as long as the Anchor Point or shape layer transforms have not been set to a different value.

ref = thisLayer;
trueX = ref.sourceRectAtTime().width /2;
value1 = - trueX * ref.scale[0] * .01;
value2 = thisComp.width/2;
t = time - inPoint;
tMin = 0;
tMax = thisComp.frameDuration * 20; // move in for 20 frames
x = easeOut(t, tMin, tMax, value1, value2);
y = thisComp.height / 2;

[x, y]

 It will work with footage, shape layers, or text layers if the paragraph justification is set to Centered. You can add the Top and Left values to fix paragraph alignment and baseline shift or multi-line problems with text layers. I have created about 30 auto-move presets that I created for animating Info Graphics and Slideshows. They fly layers in, bounce them to a stop, then fly them out or scale them out of the comp frame, always going to whatever position you place them just using the in and out points of the layers. 

If you are fairly good with expressions, you should be able to modify that expression to move layers down from the top, up from the bottom, or in from the right. You can modify that expression, so the left or right edge of the layer stops at a specific spot in the comp or the layer's original position. 

I hope this helps.

tWid=thisLayer.width;

tInc=2;

if(mX < tWid)

{mX=Math.floor(timeToFrames(time))*tInc}

else

{mX=tWid}

[mX,value[1]]

Of course this could be poured into a while() loop to potentially avoid the animation jumping and of course the time variable may need expanding to account for inPoints and whatever else you are doing.

Mylenium