What do you mean by a contract for just minutes and texts? Does you plan include any data at all, or do you get charged as you go for any data used? Most plans will give you at least 200 MB of data per month (which isn't that much).
Your smartphone is designed to access the web on a regular basis to update various bits of data. If you only want a phone for texting and calls, you may want to consider trading it in for a flip phone (which still exist).
In the meantime, you can minimize data usage by doing the following:
1. Keep mobile data OFF. Go to
Settings>Data Usage, and switch Mobile Data off. This is the surest way to prevent your phone from using any mobile data minutes. You can also tap the Menu button here and check "Restrict Background Data," which will prevent apps from refreshing data unless you're connected to wi-fi.
2. To easily toggle mobile data on or off, install a toggle widget like
Data Enabler Widget. After installing, place the widget on a homescreen (remember that it's a widget, not an app, so you need to look for it in your Widgets screen), and then you can turn mobile data on or off by simply tapping the widget.
3. In the Google Play Store app, go to its Settings, and select "Do Not Auto-Update Apps."