There really should be an option to choose more than one school.
A wizard can live without most schools but if you ask me, a wizard who chooses to lose either Abjuration or Transmutation (the one I ended up choosing) is either stupid or suicidal. Transmutation has lots of essential spells: Magic Weapon, all of the stat buffing spells, Haste, Slow, Greater Magic Weapon, polymorph self and other, Mass Haste, Teleport, and Time Stop. A wizard without any of those capabilities isn't really a D&D wizard.
Losing Abjuration would be almost as bad. Shield is very important. Dispel Magic and Greater Dispelling are essential past 6th level. Stoneskin is handy (although you could do without it) and Mind Blank is a spell every 15th level wizard ought to have running 24/7.