Correct me if I am wrong, but smart TV's are just like other TV's except you can get online for things like Hulu and NetFlix or even browse the Internet from your couch on a big screen, right?
What I did instead is buy a normal 1080P TV set with multiple HDMI ports in the size that fit my room best, them bought a refurbished Dell small factor computer with Windows 7 (that I upgraded to 10 for free) and set it along side my TV cabinet with an HDMI cable to the TV on the wall.
Now I get everything a smart TV offers, but I paid less for the TV on sale and added the Dell computer for $118 plus $5 for the HDMI cable. I think it gives me more control than a smart TV would.
You are correct in your description of what a smart TV is. I'd also like to add that many companies are also creating other devices that can sync up with other wireless devices, like a smart phone or a wireless laptop that enables this type of setup without as many of the cables cluttering the TV area. For example, Google's Chromecast is a small, wireless device that plugs into a TV's HDMI port and connects with some other wireless device in order to access the internet on the television.
Last year when I bought my smart TV, I paid about the same amount as a friend that purchased a regular HiDef TV and a Chromecast device; I bought my smart TV after waiting in line in the wee hours of the Friday after Thanksgiving while my friend was able to save the hassle of the after Thanksgiving crowds by making their purchase completely on-line and without any special sale. Looking back, I wish I had gone that route instead.
You may want to consider making your TV purchase either in November or the tail-end of January; Nov. of course for the after Thanksgiving sales, but Jan. also has great TV deals partially to decrease inventory of those not sold during the holiday season, but also as people get ready for viewing the Super Bowl.