I have been hanging back thoughtfully reading the posts here. So far everyone has a good idea as to what the ship should and shouldn't have. However, I would like to toss in a thought I had a couple of years ago.
This show, for the most part, was to be about the founding of the Federation. Politically it makes sense for the founding worlds to come together to fight a big bad evil but what would keep them together afterwards? What would keep them from going back to squabbling amongst themselves? In my opinion, it would take something that would put each of these races on the same footing and make the benefits far better than going at it alone. My first thought: sharing technology and resources. Not only would it open up trade and commerce but it would also help solidify the Federation as a power. So instead of the NX-01 going out with all of this technology, I think it would have been better to have her be rather rudimentary but with one big piece of pie to offer later to the other founding Federation worlds. (My choice would be the transporter.) And as the Romulan threat became more significant, you could have the Vulcans provide everyone shields, the Andorians phaser technology and the Tellerites could bring photon torpedoes.
So to answer the OP's original question, no shields. The NX-01 was too advanced as it was. I don't even think she should have had turbolifts. Can you just imagine the crew climbing up down all of those ladders and tiny stairways?
This show, for the most part, was to be about the founding of the Federation. Politically it makes sense for the founding worlds to come together to fight a big bad evil but what would keep them together afterwards? What would keep them from going back to squabbling amongst themselves? In my opinion, it would take something that would put each of these races on the same footing and make the benefits far better than going at it alone. My first thought: sharing technology and resources. Not only would it open up trade and commerce but it would also help solidify the Federation as a power. So instead of the NX-01 going out with all of this technology, I think it would have been better to have her be rather rudimentary but with one big piece of pie to offer later to the other founding Federation worlds. (My choice would be the transporter.) And as the Romulan threat became more significant, you could have the Vulcans provide everyone shields, the Andorians phaser technology and the Tellerites could bring photon torpedoes.
So to answer the OP's original question, no shields. The NX-01 was too advanced as it was. I don't even think she should have had turbolifts. Can you just imagine the crew climbing up down all of those ladders and tiny stairways?