You can request it when you set up your account, and it does need to be done through Customer Service; you can block individual items through MyVerizon, but the total access block is done through customer service.

You asked - "Do you also know if there's a way to allow all texting, but block all Internet access (chargeable data items)?"

The short answer is NO.  I will not put the total access block on our lines because we DO use the picture messaging - to each other, to facebook, kids to and from friends (of course, "kids" in my case is 18 and 21....).  So when a stray MB charge crops up because of an inadvertent menu choice (I have most everything blocked, but browsing the media store just happens now and then) I have been refused a credit because I will not add the total block.