Congratulations on your purchase!
Do you not ever plan to tow it, or just not yet?
For the jacking, you want to do the LIFTING on the plate that your axles are mounted into. The other jack stands you put under it will be supporting (like a leveling jack), but not lifting. You can put these jack stands where the A frame meets the body in front, and where the main frame rails come out of the back to meet the bumper. You can use a heavy duty automotive style jack stand under the axle mounting plates, but you only need a light stabilizing jack under the far ends. You can buy a set of aluminum stabilizing jacks for like $20-30 that have a light aluminum base and a screw that adjusts up to meet the frame rail.
Typically your electrical system is dual. You have a 120v system that is powered up when you plug your umbilical into the wall. This powers the 120v outlets, the Airconditioner, and the converter. The converter charges the battery, and the battery provides the 12V
power to the 12V
system. You may see some automotive "cigarette lighter" 12V
outlets around the interior, plus your lights and vent fans will run off of 12V. If your trailer still has the old blue univolt converter, you will want to replace it with something modern. You also want a deepcycle battery. Now if the previous owner has made dramatic changes to the systems, you might have something dramatically different. If you don't know anything about electrical systems, then hiring a professional is a good bet. If you want to be able to run your air conditioner, and everything in the trailer with it plugged into your house, then you will need a 30 amp plug and circuit wired up at your house.
Clean the exterior with soap and water and a non-scratchy sponge/cloth.