Best bet would be to replace the crank seals and inspect the carb flanges [rubber boots] for any cracks and replace them if needed.
A top end kit will cost about $60.
Cometic or Winderosa are the best other than OEM.

 

It is critical to make sure all the air is purged from the oil pump. There is a bleeder screw on the pump, loosen that until oil flows. That will still leave the lines going to the carbs without oil. Every time I have an issue with an oil pump. I pre-mix the first tank of gas with oil to make SURE there is going to be enough lubrication. It's cheap insurance. When you start the engine, pull the oil pump arm manually with a wire to speed up the oil flow. That will help with the delay in the oil getting to the carbs. But if you pre-mix that first tank of gas, it won't be an issue. If after your first ride, the oil in the reservoir has not gone down, you know you have an oil system issue and you can start troubleshooting to find what the problem is without having to buy new pistons/cylinders.

Mikuni round slide carbs are simple to clean. Look in the "how to" stickys and there is a really good series of pictures to help guide you. Pay particular attention to the pilot jet circuit; the air and fuel passages in the carb to the pilot jet are very small and get clogged easily. Sometimes you will have to use a wire (I use a single strand from a 4-wire phone cord) to "floss" out the junk. Most of the time I have cleaned carbs, I have not had to buy any replacement parts. Just be careful taking the float off to access the inlet needle. The arm the float is on can break if hit hard enough, which will pretty much render the carb body useless.

Lots of smart guys here when it comes to those mid-90's Cats. Keep posting, you're sure to get some great advice!

 

If you are trying Not to invest any money just to get it to run, the orings can be reused, the base gaskets are questionable? I've reused the orings with just a bit of grease. I have seen people use a thin layer of permatex on base gaskets.
The carbs can just be cleaned, pay attention to the pilot jets as stated above (up in the tube), a std 1/4 straight screw driver will work best once you grind the edges down to fit!