Congrats!
Try going to your county's assessor website. Depending on the county, you can do a map search of the parcels in your area. Figure out what the parcel/tax lot number is, and that will give you the plat map, owner, ownership history, tax history, assessed value, sometimes even cool old photos of the land and how it was used.
If your county doesn't have a good website, go "downtown" to the assessor and get some help searching.
Leases for crop or pasture are much like any other rental. Terms, price, conditions etc.
If you plan to rent the land as pasture for cattle, be sure to have conditions in the lease about fencing maintenance, water access and availability, farmer's access to the land, hours of access, hunting restrictions, liabilities, that sort of thing. You may even want to put in some language about HOW the land is grazed, how intensively etc. Are the cattle finished on the land or do they spend their whole lives there? Are they moved around in paddocks to improve grazing quality or just left to loaf and degrade the quality and cause erosion? You want to make sure that the quality of the land is preserved, not just extracting value(mining) from some inert thing(that is, if that is what you value). All those kind of things.
I bet you can find local, relevant information on rates for AG land as well. Perhaps you can get more money renting to a market gardener, hunters, wild edible foragers, who knows? If the land was rented to a grazer for a long time, chances are decent they are now underpaying for the grazing value. If it has been used as pasture in the past, it's likely that that is the best use of the land, but that is totally up to you.
Check out acrevalue.com for really good info on the types of soils on your land, use history, soil quality index, and that kind of thing.
Good luck!
-fixie