You could turn invisibility on and off as you like and there would be no time limit. Your clothes would turn invisible too, and you could decide whether the items you are holding would be visible or not.
There would be no limits on how many times or where you could teleport. The items you hold while teleporting would be teleported too. You would also have the ability to know if the place would be safe to teleport to, so you wouldn’t teleport and get impaled by an icicle or teleport inside a wall and get your insides filled with concrete or something.
Personally, I don’t know which one would I pick. Invisibility would be awesome for pranks and stuff, but teleportation probably would be more useful for everyday life.
You’re wayyy over complicating it, invisibility is just a matter of taking the light that hits you, bending it around you and putting it back in place. We can already do this on a small scale with fixed stationary setups.
Even simpler is just a very accurate and fast camera/display system that records and displays the background onto itself.