In selecting a rear dérailleur, the first consideration is how wide of a gear range it will be required to shift. Most 10-speeds have the same high gear (52 teeth on the front with 14 on the rear). The major difference between types of gearing is in how low the lowest gear is and what kind of spacing is used in between.
Dérailleurs usually are rated in terms of "tooth-difference capacity," a number that represents the dérailleur's capacity to take up slack in the chain. To find the minimum tooth-difference capacity needed for the gearing you have selected, subtract the number of teeth on your smallest rear sprocket from the number of teeth on the largest. Do the same for the front sprockets, and add the two numbers. For example, if your rear sprockets run from 14 to 26 teeth, the rear difference is 12. If your chainwheels are 36-52, the front difference is 16. Adding the figures for front and rear, we get a total difference of 28 teeth. If you get a dérailleur with a 28-tooth capacity or more, it should handle the range. If you use a dérailleur with insufficient tooth difference capacity, the chain will be too slack in some gears or too tight in others and you probably will not be able to get it to shift properly.