"Either" simply means "one or the other, when it does not matter which" and works fine at the beginning of a list of choices. "Any of" would also work.
As for punctuation, there are three traditional ways of punctuating:
... A or B or C
... A, B or C
... A, B, or C
The extra comma in (3) is called an Oxford comma and whether to use one or not varies from style guide to style guide. You should check with your editor if you are publishing or your professor if this is homework.
The option in (1) is much less common in formal writing but has its uses in creative writing. Using "A, or B, or C" is the least common and one of the other forms is almost always preferred.
I recommend (2) or (3).