A few questions to help nail down possibilities of what may be happening....though this is four days later and it may have resolved by now.
You said you just signed up...did you port your number from another carrier? It can take a few days for the port to fully resolve and all the features to start working properly on Verizon's network.
Are you in a marginal or extended service area for Verizon? Try dialing *228 option 1 (unless you have an Android, but posted in the Basic category I'm assuming you have a basic phone) from the new phone to re-align with the network where you are.
And be sure you and your friends are using full 10 digit (with area code, NO leading "1") phone numbers when sending text messages.