Yes, service availability is a real thing. Where my parents live, Verizon is the only available national provider. 8 miles to the south, ATT is also available.
$50 per month will probably get you unlimited calls and unlimited data. Cheaper options should be available, especially with third-party partners like Mint Mobile, for example. Purchasing the phone is easiest (and most expensively) from Verizon. You can get them elsewhere, like Best Buy or other electronics store. I would stay away from Ebay and other online-only places.
Assuming you have a broadband internet connection at home, you will not need unlimited data for the phone if you do most of your internet usage at home or at other places that have free wifi connections.
Yes, smaller cities and towns will have few ride options. Yes, Dial-a-Ride does has its scheduling rules.
Locked and unlocked refers to how strongly tied to the service provider you phone is. Locked means it will only work on your chosen provider (Verizon). Unlocked means it will work on all networks that your phone physically supports by the built-in radio frequencies. If you buy the phone from Verizon, it will be locked to Verizon until you have finished paying off the phone, assuming you pay for it using monthly payments instead of paying for it completely all up front.