Lovely plans...
If I'm reading that link right, I'd stay away from their 65 plus plans. The most basic plan there (200 anytime minutes, unlimited texting, and 2 GB data) looks to run $80. The standard Verizon plan (unlimited talk and text, with 1 GB data) runs $50 plus cost of the phone. You can even step up to 3 GB data for $65.
It may depend on what phone you get, but just got my Mother in Law signed up with a Galaxy Core Prime on device payment plan and the 1 GB Verizon plan for $57 plus taxes and fees. So look at all the options available, even if you qualify for a senior citizen plans.