Most of my own 'phone and all Internet use is by landline - I need a proper computer with real screen (19") hence may as well have full broadband service.
My portable 'phone spends more time switched off than on, and left at home when I go out and will not need it. I carry it on long journeys for emergency or car-breakdown use. It's off in the many situations or places where regulations, practicality or etiquette demand it be off, and overnight. (Obviously OFF when I am driving.)
It has no Internet connection. In theory it could have but I have not tried that. It would need an expensive contract rather than PAYG, but even if still possible (only about 5 years old, but 3G) it is too small physically.
I dislike text messages. I keep those to absolute need, minimum in number and length. My 'phone's primary function is speech, text a physically awkward second.
Its few accessories include an alarm I use no more than once a year, if that, and a low-quality camera I've hardly used. (My bedside alarm clock at home is a combined radio / clock.)