Welcome to the forum. This more properly belongs under lawn tractors, but that is no matter.
You will want to change all fluids: 3.2 quarts oil, 6.1 quarts kubota UDT, 3.5 quarts radiator fluids and all the filters (1 oil filter, 1 trans filter, 2 fuel filters) and clean the trans screen.
The thing has grease points all over the place (2 at end of rear wheel axle, two inside tire rear axle, front axle, etc). 9 total.
When you get under it, check to see how much play there is in the drive shaft universal joints...if there is alot of play you will eventually have to replace the drive shaft ($220, I just did mine at 1350 hours).
The unit has 3 safety switches...one under the seat (stops motor if blade going, no wieght on seat), one for the clutch (must depress clutch to start), one for the mower engage lever (must be forward against switch to start).
I disengaged the one under the seat (just put a wire across the plug) because it was getting old and when I leaned the engine would start to cut out. The other two have periodically gotten stiff, nothing that a little bit of oil and working the switch couldn't solve.
There is a screen infront of the radiator that will get clogged and drive up the temperature of goign through loose stuff...clean it periodically.
Air filter should also be changed, although it can be blown out and made serviceable.
Check belts too, of course.
Other than that, the machine is a little beast. I can run her through a field of waist high grass and she will cut through it.
Enjoy.