So I want to buy ....
A new one implies you will buy one and you don't know which one yet.
New one this looks good but how many are you buying? We need a definite or indefinite article to tell us how many we are buying.
My new one the reason my does not work is it isn't yours until you buy it.
Some new one some implies many where one without an s implies only one so this is wrong.
That is why
A new one is the answer.
A one means there is no special one. We are talking about a special or one particular book so this is wrong.
It doesn't work here because while it means the same as one, after as, and before a full thought, this is clumsy use.
Which doesn't work here because as took away the object subject connection between the phrases.
The one (that) means book modified by so exciting and from last year as in one specific book.
The one (that) is the answer