Well, guess I will jump in on this thread since we have raced the KX125 for some time.
1. DO NOT SLEEVE THIS MOTOR!!!!!! You will hate the sleeve, and once it's done, you can't go backwards. Replating will make you much happier with the power. Also, the cost is very close to a sleeve.
2. Change the dry side seal immediately, as a bad seal will cost you a bottom end. On the early 125's, I used to change the seal every month, but they are cheap, so it wasn't very costly. If you are not using race gas, you should be able to get away with changing the seal once or twice a year. These little guys can be changed by just pulling the stator plate, so it just takes a few minutes, and you don't have to split the case. It's better to spend $10 on a seal twice a year than $400 on a new bottom end.
3. The power vavle needs to be cleaned on a bike this old, so don't bother even checking. I think I wrote cleaning instructions some time ago, and Paul can help you find them if they are out there. If not, I can write instructions if needed. As mentioned in other posts, this power valve is similar to others on larger KX's.
4. The Wiseco piston will work just dandy in this unit, but wait to purchase the piston if you are going to replate.
5. 125's do not like clogged silencer, so repack just to be safe.
6. All of the rear bearings need grease, so in process of painting the frame, regrease all the bearings in the rear with a good quality water proof grease. Also, pull the bearings out of the rear hub (there are only two bearings on this year bike), pop the seals out of both sides of each bearing, clean the bearings, and regrease. I replace the grease even on new Kawasaki bearings (I installed new bearings in the rear hub of the 500 two weeks ago, and didn't bother to install until I washed the new grease out and replaced with better grease). Since these bearings are pretty cheap, you might even think about getting new ones, but use factory Kawasaki bearings, not the after market stuff.
7. Change the oil in the front forks. It's probably way old, is easy to change, and doesn't cost much at all. I think I have instructions on this somewhere on the site as well.
Well, that should do for starters. Others have said to check the timing and the spark plug. Make sure there isn't any electolisis between the plate and the case. If so, just clean off the contacting surfaces with sand paper. I have always run the NGK BR8EVX, even on the 125's. Except for the piston and cylinder work, you shouldn't have much money to spend.
Enjoy your new toy.
Rick