I agree with beets, first and foremost get some ground cover going to hold the soil in place and prevent erosion. If possible windrow the brush from side to side on the hill, which will help erosion also. I would not burn the brush, but windrow it in this fashion maybe a few rows before you gt to the bottom, leaving enough room in-between each to make a few passes with tractor and bush hog. This time of year I would probably be looking and sewing generous amounts of winter wheat or maybe a annual ryegrass. beets is correct without proper soil you may not have the best yields, but if you can get something started that is the important part. I think it is best to get even a poor stand of grass started now rather than wait a year to get everything just right and some new equipment to do anything. By then you will need a good front end loader so you can scoop up all of your dirt at the bottom of the hill and carry it back up on the hillside.
My suggestion for now. Visit your local co-op, ask what everyone is planting or what is recommended for this time of year where you liver and spend a little $$ on seed, and a hand seeder for that small area. get seed on the ground. You may not get a real good stand, but it may be enough to hold things in place through this winter. that will buy you some time to get the proper soil test and really make a long term plan for permanent pasture. Then spend this winter with a chainsaw and windrow the brush as I described earlier. You do not want to get to spring and let all that trash be left strowed around, you will tear uo a good tractor trying to bushhog over unknown trash strwoed around and the brambles will grow up and you will just have a mess, that you can not do anything with until next winter when all the brush finally dies and you can see to do something again.
That is my suggestion anyway. On that small area and it being on a hillside a good chainsaw and a helper will do more good than a tractor at this point in my opinion.
BTW, it is a nice looking place, keep us updated with your progress, I wish you the best of luck.