Generally, the "Smart" TVs require either a cable or wireless connection to the internet. If there is no internet connection available, the Smart features do not work, but everything else does, just like a TV set made in 1990.
For a long time we had a "Dumb" TV, but we connected it via a HDMI cable to a "Smart" Blu-Ray disc player, which was in turn connected to the internet through a network cable. That meant we effectively had a Smart TV. We used it mainly for Netflix. Note that many of the "Smart" TV offerings are to paid streaming services such as Netflix, Hulu, Redbox, and Amazon Prime (with more coming every day). I believe we are not too far away from the day when all TV content will be provided through streaming services. Then you will be able to watch anything you want whenever you want. AT&T is well on the way to doing just that.
One important thing for any new TV purchase is that it should have at least three HDMI ports. Not all do. Sooner or later you will need them.