Infinite; an infinite universe (unbounded metric space) means that there are points arbitrarily far apart: for any distance d, there are points that are of a distance at least d apart.
Finite; A finite universe is a bounded metric space, where there is some distance d such that all points are within distance d of each other. The smallest such d is called the diameter of the Universe, in which case the Universe has a well-defined "volume" or "scale."
There's an infinite amount of space/energy, however a (most likely) finite amount of stars, planets, etc.
Of course, taking a stance at all is a bit ridiculous with the current lack of evidence, but I am going to form my opinion based off of the past. If one were to assume that the Earth went on forever before evidence, they would be equally as justified as people claiming the universe's infinity. It makes the most sense to assume that some sort of repetition occurs where traveling distance "d" in one direction will leave the person traveling at the point at which they started.