Furniture Re-do Advice Please

I recently inherited my parent's dining room table.  That is to say, they were getting rid of it and I decided I'd like to keep it.  My grandmother, who recently moved into a retirement home, passed her dining set on to my parents.  And, thus, their table became mine.

My parents bought this table in the 70's at an auction.  The table was old then.  I'm guessing 40's ?  It's been the dinner table all through my childhood & into adulthood when I visited my parents for meals.  But, I didn't remember what it really looked like.  My mom always had it covered with a tablecloth.  Once I really saw it again, I loved it!

The top was rough, so the first step was sanding down the tabletop.  I even bought a power sander.

My plan was/is to make the top a slightly lighter shade than the original color on the bottom to give it a 2 tone effect.  The wood grain really is lovely.

As it turns out the wood grain is also a thin veneer which is chipping in places.

This one is in the center of the table where the table opens for the fold up leaf.  This one is 100% my doing.  I got a little aggressive with the sander and it chipped it on the edge.  This is about and inch/ inch 1/2 long.

Then there are a few spots like this around the edge that I just tried to sand down a bit.

There's another spot where the veneer is chipped similar to the first picture.

I have no experience with this in my furniture re-do experience.  Is there a quick and easy way to repair this?  Or do I just go ahead with staining and poly and leave those imperfections for a 'rustic' look?

I'd love your advice on this one.