If your providers don't like the valid "webcams are all sold out, so I can't buy one" excuse, then I like MM's suggestion of a Kindle Fire if you're okay with spending $50.
Cricket is a cheap phone. You can also go w/ a used or refurbished phone.
The only problem with smartphones in general is that you're likely going to have to pay for a data plan, and the cheapest I've seen (from my quick search) is $30 a month on Cricket Wireless. I just don't know how easy it is to buy a smartphone w/o buying a data plan. I mean, I know that you don't NEED to have a data plan in order to use a smartphone, but it's just that some companies will force you to buy a data plan when you buy the smartphone, if that makes sense. (This is how they make money, after all!)
But let's say you do buy a phone for like $20 and a data plan for $30. You're at $50 for your first month. A Kindle Fire is $50 on its own and you don't have to worry about data plans. You can just use your wifi in your home.
You can, however, call around to see if some place like Best Buy or Wal-Mart is willing to sell you a smartphone w/o a plan. I would give that a shot and see where it leads you. Worst case, you can fall back to a Kindle Fire.
Oh, and if you want to text people on a smartphone, I would recommend downloading Telegram or What'sApp. They are free to use and they utilize wifi. You do not need an expensive data plan to text if you go that way.
Edit: Amazon also offers monthly payment plans --
https://www.amazon.com/b?ie=UTF8&node=15281868011
I am not eligible for a payment plan, but maybe you are...?