I would only cut down the trees over ~24" diameter, or maybe over 50-60' tall. Just use the excavator to dig the stump while the tree is still whole, it makes it SO much easier to pull the whole stump out of the ground when you have a couple tons of tree leveraging it out of the ground. Then you can cut the stump off once the tree is out and laying down. Seriously, this will save you a LOT of time in getting the whole clearing project done.
In the past I did it your way, cut the trees down first and deal with the stump later. In this case, I would cut the tree as high as I safely could operate my chainsaw without standing on a ladder of something dumb like that. Safest way is still to use the excavator to knock the tree down whole by digging it's stump out. You have a lot of control as the roots get cut away; can periodically stop digging and do test pushes on the tree. Like any felling, its best to check the natural lean of the tree and go with the flow.
Edit: I essentially agree with Carl. But I get nervous trying to stump dig huge trees - they weigh too much to control with a little rental excavator, and the last thing you want is it falling on YOU or the machine you have to pay for. Depends on your machine size.