Any advice appreciated. Thanks. I'm in Zone 6 Connecticut...

Trees have been pruned, some removed, soil balanced with lime, moss is
gone, thatch is gone, brought my lawn back to life with Scotts
products, crabgrass gone, broadleafs gone. Things are really looking
good, thick and green now. It cost a pretty penny, but the results are
well worth it in my opinion. I have the best yard on my street! My
neighbors don't believe that I did it all myself! They use Chemlawn
and think I do too! Heheheheh...

Now, the moment I've been waiting for; overseeding (in the Fall of
course). Overall there are scattered barespots everywhere (not big
enough to till up, not small enough to use PatchMaster) so an
overseed, I think, is the best way to go. I was thinking of taking
this approach: in the Fall, scratch/rake up the whole yard, core
aerate, seed with spreader, and starter fertilizer.

2 questions however: 1) what's better to put on top of this,
straw/hay? Or I've seen this new green pellet stuff that expands too.
Or nothing? 2) Regardless of what I put on top of it, how should I
handle mowing? I have a decent sized tractor and am worried that I
might scatter or damage what I put down (i.e. the straw/hay/pellets
will get hacked up won't it?). Should I mow at a higher setting? Bag
or mulch (I usually mulch)? Don't mow?

Thanks folks!