If using the Specialist wizard variant from Unearthed Arcana (page 59 in the book), does the wizard need to choose one or more prohibited school(s) of magic as they are already sacrificing their familiar?
Yes. Quoting from the SRD (just because I don't have the book to hand):
Each specialist class has three variants: one that replaces the specialist's summon familiar ability
The specialist gives up something additional in order to get the listed benefit (e.g. resistance to energy for an abjurer). They still have to select prohibited schools in order to get the "regular" benefits of being a specialist wizard (extra spells per day, etc). This applies even if the benefit chosen is that which gives up the extra spells per day - in that case, the wizard has essentially gained the benefit in exchange for taking on the prohibited schools.