I would completely agree with having someone qualified to assess the parcel to be harvested check out the site, if at all possible. I know its not all that complicated, but for thinning and harvesting, its a bad move to leave that to the logger or whomever will be doing the work.
Other concern, damage to trees that will remain, along any and all skid paths, or where equipment will travel, compaction of root systems, or whatever may be specific to the site. Soil disturbance, ruts, and or restoration of same may be applicable to find a common ground on too.
Loggers can be sloppy and careless, as I have noticed, not all, but those that are I would avoid if possible.
Tops and any other wood that may be good for firewood, central piles or some agreement is desirable, at least make it accessible. When "wringing" out a scope of work for something like this, sure you don't want to choke the contractor/logger with so many details about the work, it will make them walk away, yet you may be able to work it out so that its best for all involved.
I've never believed that a little restoration on the way out, with some consideration for organization, for the tops and other wood cut that will remain, would be any significant additional cost if its planned ahead and done periodically as the job progresses if done in a manner that's efficient for the logger.
I think the worst thing is not dealing with these things up front. If you can't do it, paying the logger an agreeable amount, for say fixing ruts, drainage and any major soil disturbances from their work, would be well worth it, same with tops and other wood, I've seen where that would have paid off, pay them for a day to restore whats been disturbed, stockpile wood that remains, nothing fancy. Logger made a mess at a friends farm, and they had quite the stand of pine and such, still do, but this logger left all the hardwood that had to be cut or was damaged everywhere, one day with the skidder and all that would have been headed up, the waste and the efforts we made to gather all of that up, far exceeded the value of paying them while still on site.
One thing I dislike the most is the damage done to trees that remain, what in heck is the point of thinning when you take half the bark off those trees skidding the other logs out ??? That happened here unfortunately and most of those damaged trees have broken off or will die off soon, and its been less than 20 years.
It took years for the canopy to cover up the holes and the under growth that came in was thick, undesirable vegetation that made the woods impassable for quite some time, it eventually died out, as the canopy filled in, but it took more than 5 years as I recall, maybe 7.