what is the best way to see apple TV on my TV

Assuming you mean Apple TV+

All the ways to watch Apple TV+ - Apple Support

https://support.apple.com/en-ca/guide/tvplus/welcome/web

When you say "Apple TV" we're going to assume you mean the subscription service -- AppleTV+.

You have a couple of alternatives -- with the exception of one, they will all cost you money.

First, depending on the age of your smart TV, you may be able to download a free AppleTV+ app. But it will have to be a pretty recent TV -- I have a 2020 Samsung which has the AppleTV app, and another 2016 Samsung which cannot get it. Has to do with the embedded software in the TV. Usually if you can't get AppleTV+ app for your TV, you won't be able to get some other streaming services such as Disney+.

Second, as Rudegar said, you can buy an AppleTV box (in HD or 4K). Price is roughly $150-$200 including tax, etc and an HDMI cable to connect to your TV. That will come with a free one-year subscription to AppleTV+.

Third you can buy a used AppleTV (Gen 3). Gen 3 boxes are available on eBay, caveat emptor. I haven't checked on the Gen 3 box for a while and I'm not sure if it supports AppleTV+ or not; I know it doesn't support some late-generation streaming services such as Disney+.

Fourth you can buy the Gen 3 box and stream AppleTV+ video from your iPhone 12 to the TV through the older AppleTV box. This solution may work now but no guarantees for the future, as future iOS updates may required the newer box for streaming.

Final caveat: the newer AppleTV boxes support an "App Store" which allows you to download a large number of services and capabilities, as well as games. The Gen 3 box does NOT have the App Store function and you can only get the services which Apple loads on the machine through software updates. The Gen 3 box supports 20-30 services (Amazon Prime, Netflix, Crackle, etc) while the Gen 4 box has hundreds.

Bottom line: there are ways that you can spend a little and try AppleTV+; but the most future-proof solution is to get the AppleTV box, either in HD or 4K.

probably to purchase the appletv box

Apple TV 4K - Apple or Apple TV HD 32GB - Apple

depending on if your tv is 4k, the 4k model will still work on an older tv though just not in 4k