You can connect any Roku device to any Roku TV. They would connect just like a Blu-ray player, game console, or cable box. The rest of your questions aren't as easy to answer. All of the Roku models are slightly different from each other, but they all look the same when it comes to the interface. If the TV is several years old then it's likely that a new device will be faster when navigating, but whether it's all that noticeable is hard to say. There's also some TVs that don't support some of the newer apps. I'm not familiar with Sanyo Roku TVs, so I can't say if that's true for any of them. Roku no longer makes any "Premiere" model, so any you see for sale should be avoided. I also wouldn't recommend the least expensive Express model and I'm not fond of the sticks, but others really like them.
Keep in mind that you will need to juggle two remotes if you watch OTA (antenna) TV or want to switch to another device like a Blu-ray player or cable box, but you'd probably have to do that whether you were using a Roku TV or some other TV. I think all but the least expensive Express model come with a Voice Remote with TV controls.
Edit:
I have to edit this since I was just in Walmart (11/24/23) and they had a pile of Premieres (3920s). That device hasn't been available on the Roku website for quite a while, but apparently it's still available new (at least at Walmart).
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