mmm... you'll eventually get their personal reasons there. Waver at least you got from the beginning - he wants to prove himself. the three houses are the three houses (much of the same way they are in F/SN though Rin evolves). the Matou guy as you put it has a personal reason for fighting. Caster being the odd man out isn't that strange considering Caster was... also the odd man out in F/SN.
the relationships will become much clearer as the show continues. do think you'll like quite a few characters though.
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"Maybe it's a tentacle, molesting the planet itself. - Aschen Brodel.