Basic service is easy so do all that stuff first.. Spark plugs, A/F, and Pre Filter, as well as the Fuel filter shouldn't take ya more then 5-10 min.. Be sure to "lightly" oil the A/F Prefilter.. "Lightly" is important, too much and you will soak the A/F and the unit won't run..
We use Koh 10-30 Oil in every unit we repair/service as it is allegedly blended specifically for air cooled motors..
I would imagine most any quality 10-30 would be fine.
Check you deck and drive belts and if needed only use OEM belts for replacement.
Try not to impact anything substantial as the deck shells are thin and the deck hangers are pretty cheesy.
Make sure you blow the deck off after each use and pay particular attention to the area around the spindles. Accumulation of dirt and grass will remove the paint and rot the deck. No need for water or a detail cleaning just use your blower when your done mowing.. In fact I highly recommend blowing off the entire unit including the area under the battery and behind the motor.
Your Hydro trans is most likely non serviceable but as long as your not trying to pull out trees or tow anything very heavy you should be just fine.
I'm not a DEERE Fan but hey FREE is always GOOD so you may as well take advantage of it..