You're not simple and neither is the question ;-)
Connecting by wifi isn't the problem. Wifi is the connection your phone makes to the router in your home or to, say, the free wifi available in many pubs, coffee shops, supermarkets, etc. You can happily connect to the wifi in Costa or Wetherspoon's and browse the web, or use other internet services, at no cost.
It's getting data over your phone provider's 3G or 4G network (from their mobile phone masts) that can get expensive if you're not careful. Even if you're not browsing the internet, some apps on a phone might be seeking out data (and costing you money) without you realising it.
For example, I've only got an ancient phone which, at best, could be called 'semi smart'. It's a pay-as-you-go phone and, because I normally only use it for emergencies, I don't buy 'bundles' which offer a certain amount of calls, texts and data. I just make a simple payment for credit. When I first got the phone I couldn't work out why my credit was disappearing quicker than I thought it should be. Eventually I realised that the phone had come with a built in app which displays the current weather and temperature where I am. (i.e. it does nothing that I couldn't work out by simply looking out of the window). However my pay-as-you-go provider charges £1 per day for any data usage which isn't included in 'bundles'. So I was being charged £365 per year just to be told what I could see by looking out of my window!!! So beware of any apps which need to keep checking for up-to-date data (such as an email app which keeps checking whether you've got new mail)
The solution to such problems is either to disable all of the relevant apps or, far simpler (and safer because there's no chance of missing an app) to disable data connections until such time as you know that you need them.
I recommend turning the data icon 'off'. You'll then have a good excuse for visiting Costa or Wetherspoon's to find a free wifi connection ;-)
However I suspect that some ABers who need to receive emails instantaneously, or who can't go more than a minute or two without checking Facebook, might disagree!
[PS: There's nowt wrong with being 'almost 70'. I'm 64,so I'm well on the way!]