there is a good amount of threads here on TBN of cleanup after a clearing.
google
keywords of what you want site:tractorbynet.com
the site:tractorbynet.com only brings back results just from this site.
suggestion click up on "images" and will more likely take you to different threads.
Tractor Attachments And Skid Steer Attachments For Any Tractor Or Skid Steer = a good spot for a newbie to find videos of different equipment and in how to set it up and use it.
youtube dig up some videos and watch some.
posting pictures of current end results of what you are dealing with would help other give better advice. so they can see the ruts / holes in ground, roots sticking out, etc...
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3pt stuff
middle buster / potatoe plow, moldboard plow, trip plow, chisel, disc, harrow / drag harrow, field cultivator, various rakes.
3pt stuff grading / leveling
box blade, rear blade, grader
for FEL (front end loader)
root bucket, grapple for FEL, tooth bar, ratchet rake, stump bucket, tree spade for FEL
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there is a lot of stuff to pick and choose from. some work better than others pending on situation. some will get stuck some will not under roots. some will go further into ground than others. some are better suited after you done primary tillage, and getting a finishing top off of the soil/dirt ready for planting. while others better at primary tillage and perhaps getting more roots out.
3pt hitch tiller for example might be a bad thing, and having roots wrap around the tines, and/or bending the tines. or the tiller might skip across the roots and not actually dig down into the dirt.
a middle buster / potatoe plow, single shank that drops further down, generally has a "shear bolt" on it. so if you do snag a nasty larger root. the shear bolt with cut/break apart allowing the middle buster to swing on up and out vs having your tractor coming to a complete stop and/or possibly damaging something (shear bolt = saftey thing), middle buster going to be slow only single shank down, and it may take a couple passes over same spot to reach a given depth.
a generic bottom plow / moldboard plow. may run up under a root and get caught. a trip plow. the plows twist backwards and out hopefully being able to keep on going.
a field cultivator, the tines/shanks kinda like a trip plow. and if they hit something more likely they can bend backwards and up and out of the way and keep going. vs damaging something.
i never had luck with a disc cutting through roots. and slide over the tops of the roots instead.
box blade with scraficer teeth. you can sink them down a couple inches. maybe buying longer shanks/scraficer teeth. but is more made in grabbing high spots and bring dirt in to fill low spots.
there is no wrong or right way, but hopefully some better ways with less hassle.