There is some deeper meaning behind Bell's summoning of these particular Servants. Other than his personal dream to have a harem, his other biggest emotion is his bond with his Familia and his family which is one of the main and maybe, the sole reason they are here.
Archer: Shirou was rescued by his adopted father much like Bell was adopted by his grandfather, Zeus. That strong memory is the reason EMIYA came to Bell first.
Caster: Enkidu and his kingdom are his family. Nothing would make Gilgamesh happier than to have them back.
Saber and Lancer: Since these two are a couple, obviously they want a family of their own.
Assassin: All Jack wanted is to have her mother.
Rider: Boudica's a loving wife and a loving mother. That is why she's so hostile against the Apollo Familia since the last time a corrupt organization entered her life, her beloved daughters had to suffer the consequences.
Asterios: Despite all the harsh treatment by his abusive father, Asterios is loyal to him.
Boudica and Gilgamesh don't get along is because of how much opposite they are to each other, in terms of how they treat their rivals with a Saberface. Gilgamesh has nothing but praise and love for Artoria while Boudica has sheer hatred towards Nero.
Gilgamesh's attachments to Lily and Gina seems off at first until you realize that the three have a lot in common, particularly how their lives were harmed by the Gods.
One poster give a possible way for Ais to somewhat reconcile the existence of the Xenos and her desire to kill all monsters.
It's possible that Syr only encouraged Haruhime when saying that the latter can still be saved by a hero because she's projecting.
When first summoned, Caster remarks that if he were incarnated, he would do something about how the world works. Later, after Behemoth Alter is defeated, he tells the executives of Loki Familia that if he were integrate himself with the world, he would destroy Babel so that monsters would roam the world once more. This is so that only the worthy, the real heroes, would survive.
While thinking of the best way to crush Ishtar, Caster contemplates having her succeed in creating the Killing Stone through sacrificing Haruhime, just to destroy it at the goddess' moment of triumph. This is an example of how alien his morality and mindset are, even when compared to mortals or gods.
the existence of the Xenos and her desire to kill all monsters.