The best thing you can do is to forget the association to "expansion" in the terms we three-dimensional time travellers tend to think of it.
It's not as much expansion as it is emergence of space between stuff.
Current evidence suggests the universe is infinite and flat, which means if you keep traveling in a straight line, you'll never come back to your starting point. There is no 'edge', there is no 'farthest distance from the Big Bang' - because, remember, ALL POINTS IN THE UNIVERSE emerged from the Big Bang, so everything is equally distant from the 'center', because the center is everywhere.
At least, that's how it worked last time I checked.
Yeah, latest observations do seem to suggest that the space is flat, but we would do well to remember that we can't observe the whole universe, and cosmology is one of those branches of science where surprises still sometimes occur, so I wouldn't put it out of the group of viable options for universe to be finite but borderless (a contained geometry like the surface of sphere, torus or even möbius strip).
The problem I have with infinite and flat universe is that it doesn't agree with the principle of universe being homogenous and isotropic, simply because there is a finite amount of matter and energy*, which in infinite space could not maintain a static average density of stuff and the universe would not be homogenous any more. It would mean that at some point you start running out of stuff and that would also imply a direction to the center point, which should be detectable as stuff moving away from a certain point rather than away from everything.
A finite, contained geometry feels a lot more intuitive to me. Of course my intuition has been wrong previously. However, when considering the most recent results in cosmology, I would suggest taking them with a grain or few of salt. We don't even really know how gravity works yet, and it's pretty important in cosmology to know that... amongst other things.
Most recent scientific results are all good and well but it's also good to keep the context in mind; gravity is the least known basic interaction of nature, and it is the strongest power in the universe in cosmological scale of things. I don't think we're well equipped enough on theoretical basis to have any finality in our knowledge of the cosmology quite yet. Particle physics, maybe, but macroscopic developement of the universe... we can make more or less educated guesses but their accuracy depends on the accuracy of models used in the interpretation of observations.
We know that the general relativity model of gravity fails at minuscule distances. Who says it can't give inaccurate results at very long distances either? The assumptions of dark matter for example rely entirely on general relativity model of gravity being accurate in galactic scale. But instead of looking at an observation that seems to contradict with the theory, cosmologists have assumed the theory to be correct and add hidden variables (dark matter and dark energy, namely) to explain the observation.
For all we know, gravity could work a bit differently in galactic or intergalactic scales than it does in solar scale. After all... doing exact measurements is sort of difficult, isn't it?
For the record - I know dark matter seems to be viable explanations to the behaviour of rotating galaxies**, but I'm just saying that from entirely empiric point of view, the introduction of dark matter (without further supporting observations) seems not unlike putting a "here there be dragons" text on unknown regions of map, or saying that the dragons make things happen this way...
*Of course you can consider that universe actually has infinite amount of energy but then you're getting into a thermodynamic can of worms that will likely eat you alive... How's about infinite entropy?
**For the uneducated - observations of spiral galaxies have been somewhat puzzling because they seem to be rotating too fast for their apparent size, especially on the outskirts of the disk. Basically, if our best available model of gravity is correct, the outermost stars should be slinging into the void at the speed they are going - but they aren't.
So there is two options; either the model of gravity is somewhat wrong, or there's more mass around galaxies than meets the eye (literally). Purely assuming that there's some dark matter that you can't observe is a bit shoddy from scientific perspective; luckily, there have been some indirect observations of dark matter since, so it does seem like a viable explanation, but nevertheless it is a good example of what could possibly go wrong when the accuracy of theory is valued higher than observations to contrary.
Dark energy, on the other hand, feels somewhat dodgy in my opinion.
