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.
With the stipulations given here (no limits on where, and ability to know if it’s safe) you could teleport to what astronomers speculate are earth-like planets. Grab some samples, head home, repeat. Maybe win the Nobel Prize for discovering extraterrestrial life.
Given that, it feels a bit one sided against the other option that would let you perv a locker room or get trapped in a bank vault when you trip a non-visual sensor.
If you could teleport anywhere, you could demonstrate the power to your region’s space agency and get them to build a pressurised container or suit that can go with you.
Teleport to the moon and grab some rocks for a billionaire to make some money, then teleport to Mars and repair the broken rover. Take whatever samples the space agency wants,or transport some materials there ready for the first settlers.
This is just the standard stuff. Once you start using your imagination, there’s not much of a limit :)