To get service from Verizon through straight talk you need to pick the correct phone. The way strait talk service works is tied into the phone. So if you get a gsm phone you will most likely get service from at&t. If you pick a cdma phone then you may get service from Sprint or Verizon.
So what to do? Ask the sales people? Wish it was that simple. Most of them don't have a clue and will just stare at you. Pick a cdma phone, no phones with SIM cards. Of the cdma phones get one of their latest offerings. When st first started offering android the phones were exclusively from Sprint. Google is your friend.
You will not get service from Verizon with the precedent. You'll have to get a different phone. Good luck.