The visible universe and the speed of light

silentpundit
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It's a hard thing to Google for, so I thought I'd ask here.

Assuming that the speed of light is constant, and we can reliably measure the distance between Earth and anything we can see in the sky.

Given that the further away something is, the more in the 'past' we are actually seeing the thing due to the speed of light, how far should we be able to 'see' before we would be seeing light (or lack thereof) from the Big Bang or before?

EDIT: Okay, stupid question. Obviously the universe being 18 billion years old means that the simple answer is 18 billion light years; but since the universe is expanding, all bets are off in a sense.

My point is essentially this: how do we know the universe is in fact finite? Theoretically, we can't see beyond those 18 billion light years (which is actually more due to the expansion of the universe), right?
 
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how do we know the universe is in fact finite?
We don't?
 

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