How can I choose a correct lug for the cable? What are the aspects to be taken into account?

The correct choice of the lug is very important as the reliability of the connection depends on it. The golden rule for this is- inner diameter of the barrel should match the diameter of the core prepared for crimping. It means that there be almost no gap between the lug and the wire. It is quite easy for lugs like ТА, ТАМ, ТМЛ(DIN), ТМЛс, НШП as the nominal size of each corresponds to the cross-section of the core. It gets a little more complicated when you deal with ТМ and ТМЛ (Russian standard ГОСТ 7386-80). You can use s special chart give in the correspondent ГОСТ standard. However, in this case, you should definitely know the flexibility class of the cable core. This info is usually no problem is you know the type of cable you deal with.
In the ideal situation, you should measure the core diameter and match it with a diameter of the lug barrel indicated in the chart of ТМ\ТМЛ made by KBT. The third figure in the name means the necessary diameter, for example, ТМЛ 70-10-13. The last figure, 13 in the example, should be very close to the diameter of the core, but not less!