I don't have a physics background, so forgive a naïve question.
Not necessarily; there are models with a spatially infinite universe and models with a spatially finite universe. In our best current model, the universe is spatially infinite; but there is enough wiggle room in the data that a spatially finite (but very, very large) model is still possible (though unlikely).
> Every time I watch a science program about the big bang they say that everything was contained in an area smaller than an atom?
They are talking about the observable universe, not the entire universe. Unfortunately, many pop science treatments don't make the distinction clear.
Yes.
> What about just bog standard "surface of a circle", aka. space in a sphere?
Such a model would not be spatially homogeneous or isotropic; the "radial" direction (toward or away from the center of the sphere) would be different from the tangential directions. But all of our observations indicate that our universe is spatially homogeneous and isotropic.
From the point of view of any observer in our universe, space/time accelerates away equally in all directions - just like a grid on a ball that's inflating spreads out over time.
But the grid has more than two dimensions.
You may be wondering what's "inside" the "sphere." Whatever is there can't be reached from the universe, no matter which direction you travel in. It's literally in a different dimension.
But that's almost completely meaningless as a statement. No one has any idea how the "sphere" really works.
In our universe we can take it for granted that space/time defines a system for measuring shapes and distances.
Outside of the "surface" of the universe, there's no way to know how shapes or distances work, or whether there even needs to be something on the "inside" - it's possible the "sphere" only exists as a mathematical template, because it's the only way space/time can hang together, and it's some kind of weird emergent thing that has to happen. (Insert further idle speculation here.)
This is all really, really hard to imagine. Brains evolved for swinging through trees can't visualise it without math. Brains with math are still very much struggling with it.