Pictures would be helpful, you should be able to glue the crack, seems like the original finish was glossy on those SKB's, probaly lacquer.
Once all the paint is off and repairs made you can wet sand with water and 220 or whatever it needs, if 220 too fine step down a notch, wet sanding with water will raise the grain slightly.
The worst part will be sanding around the checkering, you may have to point that up and good luck.
Boiled linseed oil is a good finish, you can add some beeswax to the BL, you will have to heat, I used a small tin and a candle, a tin like from a shoe paste top will work.
You can wet sand with the linseed oil as well, warming the stock and oil helps to absorb the oil, rub vigorously!
