Not sure if you can borrow a disc, which is my favorite tool and requires the least amount of tractor horse power. Just lightly disc the field, making lines in the dirt, not returning field to dirt. Stubble left on it is fine, helps prevent washout in rain runoff.
Broadcast seeding works, just need a PTO on the tractor to throw the seed. I attach a chain harrow, teeth down, to follow the tractor. If ground is pretty firm. A couple old tires tied on the pulling bar will help hold the front teeth on the ground to spread dirt over the seed as you go.
This is the big broadcast unit that fits behind the tractor seat.
A seed drill will require a live hydraulics on the tractor to “drill” in the seed. Local rental grass drill need a 40hp tractor to run the drill.
A note on seed, is to spread the small seeds, then the bigger seed (like brome) by itself. Mixing your seed can cause clogging problems as various seeds all try to get thru the holes at once. You can waste small seeds as they run out like water! Not spread as thinly as seeding rates suggest. Then you have to buy more seed for the places not seeded. This does mean a few more trips across the field, spreading the seeds individually. Buy quality seed, perrenials, in the north. They come back every year.
Getting with your local Extension Service will give you local information on soil types in your area, seeds for pasture that are successful in those soils, planting dates.
As already mentioned, start with a soil test with your “crop” being grasses. Fertilizer adds nutrition to your grasses. You probably have plenty of nitrogen after a soybean crop, but need the other nutrients added. Tell the fertilizer folks you do NOT want urea as a nitrogen source, if you need nitrogen. Urea is not healthy for any hooved animals to be grazing on, they can founder. I use Ammonium Sulphate as my nitrogen source, has no issues for grazing animals.