Will you shave your whole neck or just trim the beard there ?

If you shave the whole neck you can use the biggest razor you can handle. Trimming is another story.
Strictly for trimming you could use a small 3/8 or 4/8 razor. They are more challenging of correct angle but for accuracy they can't be beaten.

Your price range would maybe allow 2 razors or you could compromise on 5/8 or maybe 4/8.