First, you don't specify which cables & specific model cable box you are currently using. Second, it would be prudent for you to inquire of Verizon exactly which hardware you will be receiving upon the service change. Their FIOS technical support web site will have some of these details for certain.
That said, it's likely you will be using the same HDMI cable that you have now, unless you are using either component or DVI, hence my first question above ;).
I currently have a 36" LCD HDTV connected thru a Brighthouse cable TV box with the required cables.
Next month I will be changing to Verizon FIOS TV with a new TV which is a Toshiba 55" model 55zv650u.
Do I need to purchase new cables for this transition or will the cables I currently use function with this new TV and FIOS.