It might be worth starting with the larger of the two Bobcat mini-excavators to get a feel for using one to remove trees. However, given the area that needs to be cleared I'd second looking at renting a larger excavator as the rental prices generally start flattening out as the size of the machine increases, even though productivity of the larger machines can be much better (especially if there's room to operate).
The biggest reason I went with a 5-ton machine was that's the size range I've considered as a potential future purchase. If I were clearing a larger area I'd look at renting a full sized excavator to make shorter/quicker, more cost effective progress. Getting one with with a thumb it should be possible to build a pile that can then be hauled with a tractor/grapple to a single burn spot. Of course, with the thumb (preferably a hydraulic one for more flexible use) it should also be possible to lift and drop the rootball/tree to knock a fair amount of dirt/soil off.
Just for the sake of providing a data point, this tree:
View attachment 612197 18 months later left this stump
View attachment 612196 ...which was the larger of the two Bradfords I removed. At the time I cut it down (the fall of the year after the spring the picture of the tree was taken - or roughly 20 months later) the limbs were touching the fence line. Taking this particular stump out took probably 1-2 hours -- that's a rough guestimate I wasn't paying much attention to time as I was having fun learning how to operate the machine (was a first time user), and figuring out the most efficient way to do what I was trying to do since the removal of the two Bradfords was the practice for removal of a ~21" diameter pin oak.
Trees smaller than these should be easier and quicker as at some point in the small tree vs. large machine equation there's a point at which the force the machine can generate should just be able to pop the tree/stump out ... much like a shovel or mattock on a small sapling. Which is where clearing a large area becomes
relatively easy & straight forward.
The other nice about using an excavator for this sort of work is that it minimizes the disturbance of the top soil to get the tree out, and if digging turns out to be necessary the topsoil can be put in one pile, and all the other dirt in another pile. Which in turn permits scooping the dirt back into the hole and putting the top soil back on top.
(It might just be me, but after a while working with the excavator I found that it was actually easier/faster to use the bucket to back fill a hole than it was to use the blade on the mini-ex to do so ...took a bit of coordination to do so cleanly, but after getting used to it, iI found it to be the preferable method of moving dirt).