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You can have spells of any school. If you have opposition school you can still learn and prepare those schools by preparing it in 2 slots.
Later you can take an arcane discovery opposition research if you really want to eliminate an opposition school.
If your a thassalionian specialist wizard you can never prepare or learn a spell from your prohibited school. You need Use magic device to activate the spell Tigger or completion item. Opposition research can not gain back a prohibited school of a thassalionian specialist.

Rub-Eta |
Yes, you can have any spell from the wizard spell list in your spell book. The point of specialty school is that you get one extra spell slot to prepair a spell from that school in (and the school powers). All in all, it's worth it. Even though you have to pick two opposition schools, where you need to spend two spell slots to prepair one spell from those schools. You won't have enough spell slots for every spell anyway so it's okay to throw two of the schools under the buss.
Here is a link to a thread with links to a really good and extensive guide on how to build a wizard.

master_marshmallow |

You can prepare and cast any spells on your spell list.
If you specialize, then any spells that belong to your opposition schools cost you two spell slots to prepare.
When it comes to choosing a school, you should pick something based on what you want your character to do. Do you want to be a blaster? Do you want to summon things? Do you want to control the battlefield? Do you want to always go first and never be surprised by anything?
Wizard is a very powerful class with a lot of options, but it is much easier to play if you have an idea of the general theme you want for your character.