We've found park WiFi to be iffy at best and that's using a WiFiRanger to boost our WiFi capabilities. At a few parks we've had very good WiFi - at most, poor to none.
Security isn't a big issue as long as you have "https" in the address. The security is provided by your web browser and the site you are connected to, not the park WiFi, etc.
A good cellular data connection is the most reliable and Verizon is the carrier with the best coverage. I agree with the recommendation of Millenicom - it uses Verizon's towers and gives you 20 gigs a month for a reasonable price.
In our case, we are on a grandfathered unlimited data plan so we use our cell phone as a hotspot.
Millenicom or your phone, a good investment might be a Wilson Sleek. You put your cell device in a cradle and it boosts your cell signal. It won't magically make a non-existent signal appear, but if you have 1 or 2 bars of poor signal it will boost it to a usable level.