Remember there are several possible uses with either neither
I want neither the first choice nor the second.
I think you can have either.

Use:
Either and neither compare two possibilities. Either expresses that both are possible. Neither expresses that both are not possible.

Structure
Either and neither can be used with or and nor although it is not necessary.
Either … or Neither … nor

Examples:
The circumstance put company into a situation where they had to decide between the two solutions. Neither seemed to be good.
Either we go or we don’t.