Short cage mech will work on 1×10 set ups running a 11-36 cassette or 11-34, will not work for 2×10 or 3×10 setups as the increased chain length required for moving up/down front chainrings can not be accommodated for with a short cage mech.
Medium cage mech will work with 2×10 (and 3×10 if you are sensible with what cog in the rear cassette/front chainring you ride in) with the remit that the rear cassette is in the range 11-34 and you have double front chainrings such as 26/39 or 28/42
Long cage rear mech will work with 3 x 10 in just about any configuration.
As you’re building up a geared tourer for the road then what mech will be best practice to fit will depend on whether or not you are fitting a triple up front or a double, if a triple up front such as a shimano 105 running 50/39/30 and say a Shimano 105 11-25 cassette at the rear then i would fit a Shimano 105 medium cage rear mech.
As you ride a singlespeed you’re probably powerful enough to ride a double on the front such as a Shimano 105 running 50/34 and perhaps a 11-28 rear cassette and for this you will be able to use a short cage rear mech.
That’s a rough idea, depends if you feel that a 34×28 will be a suitable low gear to get you up the hills with a laden down tourer at the end of a long day on the bike.
