looking at satilite image, and judging trees near the houses vs what you have circled. it looks like all small size trees, that would be to small. to do much with. exception might be, cutting the trees up to turn them into wooden fence posts. assuming you can get enough straight length. and the trees could make good fence posts.
not sure if it would be worth while to really "cut" and if need be split the wood for "fire wood" and then sale off the firewood.
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as far as making the area ready for field work. i would say, get the roots out now. there are multi ways to take trees down and get the roots out. but you have so many trees, that it no longer becomes what you have, but rather what would take least amount of time. and do a good job at it.
the other issue, is re-grading area were trees were, and dealing with any swamping areas / rutted up areas. and in that moving dirt in to fill holes were tree roots were. to getting good run off water drainage on the field. so you do not end up with major wash outs, within the years to come.
with above said, my vote would be dozer work. dozer can push the smaller trees down and get the tree roots at same time. then go back over the areas and push dirt back into holes and regrading everything. so you end up with nice smooth transitions on any hilly areas. or perhaps flatten things out better for you.
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if you already have a good size tractor, you could get a 3pt hitch with subframe backhoe for tractor. and remove trees that way fairly easily. and then use FEL (front end loader with heavy duty bucket), and 3pt hitch box blade with rippers, to regrade and level things out as well.
the backhoe, with FEL, and box blade for say 50 to 60 HP tractor. with R1 / AG tires on it. could have long term benefit for you. for other projects on the farm. from grading dirt and gravely driveways, to dealing with trenches, to pulling old fence posts, if your state laws allow for it on your property to possibly dig a hole and bury a dead horse / cow / other live stock deep enough and properly. and tractor could possibly be re-used, to pull plow, disc, harrow, planter possibly. (depends) some times it can be better to have a tractor setup for just field work vs jack of trades tractor that does a little bit of everything.
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not knowing other stuff (all acrage you have, and any other tractors you might have). i would say get a tractor with backhoe, were you can move a lever and swivel the seat 180 degrees to operate backhoe. and make sure you can remove backhoe. so you can use other 3pt implements. this rules out good amount of "industrial" TLB (tractor loader backhoes) that you might see city workers using. and as a result puts you more in utility class tractors. that are built more directly for a backhoe operation.
you can place a 3pt backhoe with subframe on nearly every tractor with some modifications to subframe possibly. but this normally requires hoping off of tractor and then going around and hoping on backhoe seat to operate backhoe. this can be rather time consuming, more so when digging a trench, but can work.
if you are going to rent a backhoe or rather a "excavator" for a few days or a couple weeks to clear the trees, you would more likely be better off renting a dozer. or just paying someone to do the dozer work.
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some tree roots. "spread out" over a large area. while other trees, tend to go straight down into the ground. you may want to dig up around some of the trees. to help remove some of the larger size roots. so plow does not get hung up on the larger size roots.
