Motor theory is a complex subject. Even when taught in technical schools, only a miniscule part is conveyed. As much because the instructors and texts don't fully understand it at the working level. I've gotten wound up on the subject several times in the past, and there are references linked in this database on the subject. The information is there, but to put it to practical use requires that undefineable grasp of what it means.
Then the subject of capacitors, a whole 'nuther ball of wax. It helps to have a founding in electronics to grasp caps. Then combine the two and you have a well of almost infinate depth. It can take years of working with them to grasp some of the finer details. I have 50 plus years experience and still only grasp a small part of it.
In any case, to the original question: A motor capacitor has two distinct ratings. Voltage and Capacity. . . Voltage is simple, use the highest that will fit in the can. For a 120 volt motor, try for 300 volts or better.Sometimes you can and sometimes you can't. But try. Higher voltage is a safety factor, It may never (hopefully) be needed. But if it is, it's there. Cheap insurance. . .
Capacity is a rather fluid measure. Most non-polarized (AC) capacitors will be rated as "plus or minus" some nominal amount. The tighter this tolerance the better the quality of the capacitor. A motor cap of a nominal 300 MFD (micro-farads) is about the middle of the range. Try to maintain that rating. The motor will run if the cap is above or below that nominal value. But torque will be lost for starting, with a loss either above or below the rating.
For machine tools, this doesn't really matter so much. But there are motors that start under load and capacity does matter. Machine tools usually start at almost a freewheeling load and the capacitor is switched out within a second or two. During that two seconds, the capacitor combines with the reactance of the start winding to create a second, magnetically offset, second phase. It is this two phase application that produces the torque until the motor speed reaches about half way.
This phenomanon can be observed in single phase, two phase, or three phase motors where a phase is disabled for some reason. Even a 100 HP, 3 phase motor can be started when one phase is open. It won't have much torque but will run unloaded simply by starting by hand. From here the rabbit hole goes deep. Try to better the voltage where possible and keep the capacity (MFD) as near original as possible.
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