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[Game of Thrones][ASOIAF] How are Kingsguard men chosen? (Minor GOT S6E3 Tower of Joy spoilers)

The problem I see is trying to find the best fighters in the realm, and yet *also*  managing to find the most loyal men who would defend the king to their last breath. 

Ideally whichever House was in power would only enlist the best of their own men, perhaps looking to historically allied houses for additional good fighters. But the chances of rolling out a Kingsguard line-up with men who have long worked for your House (and or in a well trusted allied House), *and* who are so skilled that the majority of Westeros's top fighters are in their ranks... Well, it's leaning towards extremely unlikely. 

During times of relative peace and comradery between the main Houses, you can have a team of Kingsguard made up of the best fighters in the realm from a variety of Houses with little to no issue. But surely someone (from the House in power or perhaps a potential usurper) would realise the problem of having so many skilled fighters from other Houses given top notch equipment and access to the home of the Royal family. Heck there are two examples of this flaw in (what I understand to be) the Kingsguard hiring checklist that I can think of off the top of my head. 

Firstly, Jaime Lannister, the Kingslayer. He had a valid reason, sure. But still, from the side of House Targaryen he was obviously a weakness in their Kingsguard due to his lack of loyalty to the Targaryen rule, ending with him stabbing the king in the back instead of following his orders. Of course to anyone with common sense, he did the right thing. But all it takes is for one member of the Kingsguard from a powerful House to decide they don't agree with the King's decisions before plotting (and carrying out) a take-over. Jaime was one of the top fighters in Westeros, but definitely lacked loyalty to House Targaryen or any house besides House Lannister (although it could just as easily be explained as preventing a massacre). 

On the other hand we have the ever-loyal Kingsguard accompanying Sir Arthur Dayne in defence of the Tower of Joy against Ned Stark, Howland Reed and their allies. This may be Sir Gerold Hightower (and or Sir Oswell Whent), but as the show leaves many of the combatants unnamed I shall be calling Dayne's fellow Kingsguard "Bob of House TBA". Now Bob TBA was certainly loyal, to the extent of accompanying Sir Arthur to the Tower of Joy and standing to fight numerous fighters (all pretty good fighters in their own right). He lacked skill though. He clearly isn't one of Westeros's legendary knights or we would have heard more about Ned facing off against Arthur Dayne *and* Sir Bob TBA. He's not mentioned in the show, and from what I understand is not expanded upon much in the books either. During the fight scene he survives for a while against Ned's band of fighters, but is dispatched rather easily and without pomp or glory once Team Ned gets back into formation. Of course, then they get deftly defeated by Dayne on his own (if not for Reed's backstab and Ned finishing him off), but my point stands. Bob was a paragon of loyalty, but clearly wasn't one of the realm's top fighters. 

So what gives? What is the process? If you were in charge of Kingsguard HR and Personnel, how would you change the system?
gpt
The official process is very simple.  The king offers people the job, and they take a standardised oath that involves not marrying, not inheriting, serving the king, and not retreating.  How does a king choose?  It depends on the king.  

Some kings want mighty warriors.  Arthur Dayne, Barristan Selmy, Jaime Lannister, all could eventually compete to be the greatest swordsman in the realm.

Some kings want good advisors.  Barristan Selmy's honour was impeachable.  He would always have a proper course of action to suggest.

Some kings want loyal men, willing to do whatever they want.  Jorah Mormont had been with Daenerys from her wedding to Drogo.  Meryn Trant had no code of honour beyond doing what his master needed.  

Some kings want to use appointment politically.  They appoint someone as a favour, or as a curse.  Jaime was the firstborn son of Tywin, appointing him deliberately slighted the man.  But to appoint a third son, or someone else seeking for glory, would be a great sign of prestige and a real chance for them to influence the king.  

Most kings realise that you can do all of these things.  You don't need every kingsguard to be a great warrior so long as some of them are: they defend a throne, not a city or even a palace.  You don't want everyone to be political, since that's a valuable carrot to offer to nobles.  Loyalty is admirable, but appointing on loyalty alone can make kingsguards weak.  Advising's only really necessary for a couple of kingsguards: the lord commander and his heir apparent.  The rest can follow good ideas.  So the king thinks about who's available, listens to what his small council says, takes under consideration the advice of other noblemen, and eventually comes to a decision.  They normally start with a kingsguard mostly intact, but if they don't, they pick up a few as they go along, waiting for the right men rather than doing things too rapidly.

Daenerys is an excellent example of a ruler who has had to set up a kingsguard (queensguard, whatever, it's the same concept) from scratch.  She starts with Jorah Mormont, a decently capable warrior who she thinks is loyal and who seems to give good advice.  She adds three bloodriders, and this is mostly political: she wants some of the Dothraki Drogo led to stay with her, but they're decent fighters as well.  Barristan Selmy is, if anything, overqualified (he can do everything but sway politics), so he's an obvious pick.  Daario is a good example of a good non-loyal choice: it's political (she wants his mercenary company), he's an exceptional fighter (he kills the champion of mereen and the guardsmen at Yunkai), he can advise (he knows the local culture better than anyone she knows), but she knows he's not loyal (he gave her the heads of his previous commanders).