JD will have all the fluids you need for it, if there is a dealer near you. There should be another port with a screw cap on it to fill the hydraulic fluid. I am pretty sure it doesn't go in through where the dipstick is at. Maybe someone else here can say for sure where it's located at, or your dealer can tell you.
I've always used the Shell Rotella T 15-w40 engine oil in my tractors. Nothing wrong with the JD brand, of course, just my preference since the Shell is more readily available. Heck, even Walmart and Kmart carry it. Try to find some JD oil there lol!
As for changing the engine oil, there is no magic to it. Just get yourself a new oil filter (this will probably have to come from JD) and enough oil. According to tractordata (see link below) the 3cyl Yanmar engine in the 855 requires 3.8 quarts of engine oil, so I would go ahead and buy a gallon container of new oil and one extra quart to keep it topped off with.
Let the engine idle a few minutes to warm up the oil, then shut it off. Pull the plug and drain the old oil, and remove the old filter. Reinstall the drain plug after the old oil has drained out.
Get the new filter and fill it about half way full of new oil. Take your finger and dip it in some oil and lube the rubber seal on the top of the filter.
Spin the new filter on, but try not to spill any. If your filter is mounted horizontal, I would place a big rag underneath it to catch whatever does spill. This is when you HATE filters that are mounted horizontal!
Refill engine with 3.7 quarts new oil (allowing for the little bit you already poured into the new oil filter). Crank it up and look for any leaks. If no leaks, you are done! Here are most of the 85 spec's:
TractorData.com John Deere 855 tractor information
