Oooh, I am thinking of starting another Four Corners save file, too! It's just so neat and cute.
You start out with the house in the upper right quadrant. This is a good space for crops in the early game, since it is right outside your front door and has a watering hole only a few steps away. (However, I only grow crops on the farm for the first two years; once I have shipped 15 of every crop, I move crops to the greenhouse and Ginger Island.)
The upper left quadrant will sometimes spawn weeds that can give you mixed seeds. I usually leave this area to run a bit wild during the early game - it becomes a nice source of wood, and once you upgrade to a copper axe, there is one stump that regenerates every day. I think I turned this into a pasture area, but you could do animals, crops, or even fish ponds, whichever you prefer.
On the lower left, there is a pond. I like to fill it with crab pots (because I dislike fishing with the rod). For aesthetic reasons, I also put a coop here (so the ducks can hop into the pond to swim). If you collect a lot of rice shoots and taro tubers, this is also a nice place to plant them (just remember to add a scarecrow).
While the mini quarry in the lower right is not very big, I would make a point to clear a path to it on day one, because it will give you a jump start on mining. You may not get much, but all you really need is to have Clint give you the furnace recipe before the mines open. Then, you can craft a furnace that very first mining day, and smelt copper bars every time you hit an elevator floor. That should give you a leg up on getting tools upgraded more quickly. I plan to move both the farm house and the greenhouse to this quadrant, as well as any pet bowls. (Note that I strongly advise immediately moving the first pet bowl closer to your house. It starts out smack in the middle of the farm - which means your pet will wander off into ANY of the four quadrants, and you will only find him/her if you get lucky.)
I have not worked out how many animals can comfortably fit onto this farm once blue grass is unlocked - I think with green grass, I had 36 animals (2 coops, 1 barn). I want more next time, so we'll have to see how it goes. I'm not a fan of processing sheds - either the machines go into my house/coop/barn, or they get stuck somewhere off the farm. There are plenty of other places to put those things around the valley.
Do you have a theme picked out for your farm? I'm finishing up my periodic table of elements farm, and I need a theme for the next one. Maybe I'll do gemstones ...