hi kevin, seems you already have some quality bulk material to make a really powerful
compost. But it does require a great deal of manual labor also to quickly condition those materials into viable compost. The first thing you might think about is see what everyone else is doing which is easy to do right here at this site:
https://permies.com/forums/f-72/composting
I would suggest a sawdust liner or base at your selected site, the sawdust acts as an organic visable distinction between the compost and the ground (or rocks in my case) below it, the sawdust keeps you from digging up rocks. It helps if your compost site is somewhat shaded (imagine digging dirt in full sun, as compared to digging under the shade of some trees~~~makes a lot of difference to me if I'm the digger! hahaa). The shape of the compost heap is fairly simple, pile it up to at least 3' tall or preferably 4' tall, it is the huge amount piled up that causes the materials 'to work'. Lots of people use wooden barriers around the sides and back, some use cinder blocks, I don't use any barriers, I just leave mine on the ground in a big heap with a thick sawdust base.
Once you have your materials piled up, you will need to 'dig' or 'double dig', or 'turn' the materials from time to time. You will notice immediately while trying to turn hay manure material, that it doesn't dig easily, because of the hay is fairly tough & long stranded. So there is more labor involved in chopping all the material in the heap, or whatever goes into the heap it is better to chop it first, a lawnmower does a great job chopping. I wouldn't hesitate to add chopped leaves from the trees, or other plants. You might not want to put lots of sticks or wood in your compost because it doesn't chop up easily, nor does sticks decompose as quickly as leaves.
If you use a lawnmower to chop your compost heap you will need a respirator mask, as there is a lot of manure in your heap already, and you really don't want to breath that kind of dust. Once you get your heap chopped an piled high, make sure it gets rained on, or add some water. On a new heap I try to make sure the whole thing is soaked all the way to the base if possible, then add some water from time to time if you think necessary. If you have some fresh cut green hay, chop that and put in the heap also. In a few days your compost should begin to heat up in the deepest areas of the heap. Once the thing begins to get hot, don't get too anxious to turn it, let it work undisturbed, except for taking an occasional sample.
After a couple weeks and you know the heap has been hot you might try turning the whole batch to mix the outside with the inside of the heap. Don't saturate with water while the thing is hot, let it work, but if it rains on it that is OK. Remember to keep your heap tall, don't let it get less than 3' tall.
Generally keep a separate compost heap for any meat or fat type materials, those materials don't 'work' the same as plant materials.
james beam;)