Whether or not to use public Wi-Fi is up to your comfort level.
If the Wi-Fi is set up properly, then it's safe to use. Even safer than connecting through your cell service, because you should have a firewall between you and the Wild, Wild, 'Net.
OTOH, I'm not sure I trust most places to set up their Guest accounts to properly isolate everyone from each other. If they don't, then someone could have a virus on their phone or laptop and not even know it. It could go try to infect any other machines it sees on the local network.
Also, the only way your phone would log in automagically is if you have your Wi-Fi set to do that. Personally, I don't want my phone logging into to any random Wi-Fi I go past. Besides, most stores and business with public Wi-Fi will they make you tap an "I Accept" button, promising that you won't use their Wi-Fi for bad things, before they'll let you use it. So, it won't log in automagically, anyway.
And, finally, do you really need to log into their network? If you are not streaming music while you're there, or some other bulky task, then the amount of data you save is trivial. Especially if it's just to pick up a prescription. Chances are you're going to be there about 15 mins, give or take. Even streaming music, that's not enough to worry about.
I would recommend leaving your mobile data connection on unless you have a really good reason to turn it off. Being connected is a lot of the value of having a smartphone. If you're connected to Wi-Fi, it'll use that. If the Wi-Fi drops for any reason, it'll fall back to your data connection. Most apps that have high data use have a setting within the app to require a Wi-Fi connection, so that you don't accidentally run up a lot of data. Use the settings in those apps to protect yourself.
Personally, when I'm at a friend's, and it's someone I visit regularly, I'll ask for their Wi-Fi password. That way, when I go there, my phone logs in automagically. But, when I'm out and about, I rarely log into any business' Wi-Fi. Because, I'm rarely doing anything more than email or light surfing.