Let's start with a compaction test. Take a 3/8 rebar stake and see if you can push it into the soil by hand 1 inch? 3? 6?
Surface compaction makes life hard on seedlings.
Next
Take a hammer and lightly tap the rebar and drive it till it suddenly becomes harder to drive or stops. 4 inches? 6 inches ? 8? maybe 12? Now dig that spot up with a shovel or post hole digger. What stopped you? A rock or soil? Find the hard pan.
Knowing these things will too you what your soil conditions are.
While you are doing this take soil samples from at least a dozen locations in the field and send them off for analysis and ph testing. Be prepared to lime your soil.
Next decide what you want to plant because the crop determines the soil needs and processes.
I have a tph tiller for my garden. They are not designed for breaking ground, only finishing plowed or disturbed soil. I have a tph disk works well in loose soil or plowed soil but not hard ground. If a disk was all I had access to then I would scuff it up best I could with that, don't destroy your tiller. When in doubt plant a blend, when building soils plant a blend. Spring or fall plant a blend. I am a strong believer in soil building and with 7 to 9 species blends you can do wonders. I also like to feed wildlife and blends can feed many species at one time but even if I plant only soybeans I plant a blend of forage beans. If you have a tph attachment for your skid steer then you might want to consider an orchard plow, a great tool for rough ground. If your field has been compacted severely you may need a sub-soil ripper to get down deep and break up that compaction. This will allow water to penetrate and be stored rather than run off and opens the soil for roots to reach that water and other nutrients previously unreachable.
Many areas have less than 1% organic matter in the soil, 3 % is considered great and 5% is magnificent and 5% would be a lofty but honorable goal.
You can also help your soil with your plant choices. Turnips run deep tap roots seeking water and nutrients opening passages in the soil. Sun hemp is a legume with a good root system, annual clovers are shallow legumes that will feed nitrogen to the other plants, buckwheat is always a good choice for roots, collard greens and radishes generate matter and are nutritious. Sorghum hybrids and corn produces a lot of matter for soil building and cover for wildlife. Beans and peas are pretty much food but do convert and save nitrogen.
Soil samples are where to start after learning about compaction. If you have highly erodible soil like I am working with on a farm in Ky you want to consider managing erosion with plants and methods. Wheat, cereal rye, oats germinate quickly (in that order) and help hold soils while other seeds germinate and develop more slowly. They are also desirable browse and will absorb pressure while other seeds get a start. I use cereal rye to protect over browsed clover in the winter. They also help protect the soil from drying effects of sun and wind and insulate soil temps.
Sorry for the book, I love this stuff. Glad to help anytime.