First, you can get the users manual, parts manual and service manual all via this site, or at Rice Equipment: 814-226-9200.
The tranny oil goes into the hole under and just in front of the driver's seat. I used 120w-90. Five gallons at Pep Boys was about $25. Manual says to put in four.
By the way, when you drain it, expect anywhere from 5 to 15 gallons to come out. Water gets in over the years and adds to the oil. It will probably come out coffee colored as a result. 15 gallons is a lot of oil to dispose of. Can surprise you.
Engine oil goes into a fitting between the magneto and the radiator. Unless you have cleaned out the engine, use non-detergent oil (so it doesn't loosen the crud and clog everything). I got that at Pep Boys too. Cheapest oil they had. Fill oil until it runs out the top petcock mounted on the oil pan. Or, just put in 5 1/2 quarts. Manual calls for 30w. Rice has oil filters. It goes into that dome shaped fitting on the other side of the magneto.
Rice is a good source of parts. Call him.