I agree with the above post that the ability to address an extreme close quarter combat situation is important. One of the old (active in the 1970s) former police offers I know attributes a number of the controversies in modern law enforcement to a decreased ability of officers to manage close quarters situations, or to manage threats without using a firearm.

That's partly a reference to an increased militarization of police officers with a consequent lack of emphasis on training officers to de-escalate situations, and partly a reference to a lack of emphasis on effective hand to hand combat skills.

Those other self defense skills should be learned concurrently with learning to use a firearm for self defense.

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Aside from the need for close quarter skills, there is also a progression of skills that need to be mastered just to handle the weapon before moving on to the more advanced skills:

1) mastery of basic marksmanship and safe gun handling;
2) mastering the ability to draw from concealment and fire accurately and quickly;
3) mastering the ability to draw and fire while moving towards cover, or while getting out of the line of attack of an assailant;

then and only then...

4) mastering the other supporting skills such as shooting with the weak hand, performing a tactical reload, clearing malfunctions, reloading with one hand, using a tactical light, etc.