Your dad's old oilstone is really not quite good enough! If you are really hard up it will do, but you will never be able to get a sharp edge and most of your work will be much harder as a result.
There are two schools of thought here: either a very hard smooth stone such as an Arkansas stone, which scarcely wears away at all and remains beautifully flat; or a softer stone made up of tiny hard particles in a weak matrix, which wears away rapidly exposing new sharp edges all the time.
I strongly prefer the latter system which is exemplified in the Japanese water stones and the Belgian stones. Either way get a 1,000 grit for initial sharpening and a very fine grit, say 10,000 grit, for final finishing. The German firm of Apex [The box says Apex-Sal-Abziehsteine] produces a very economical double-sided stone which does both jobs admirably.
All these stones, whatever the system chosen should be used with water, not oil, as a lubricant to wash away the swarf out of the pores of the stone.