Many many years ago I borrowed my Mom's Datsun 310 (Yes, THAT long ago). She told me to be sure to refill it with "good" gas before I returned it. Hopefully from the local Exxon station. Being in the habit of running my vehicle on the cheapest gas possible I ignored this request. Yep, she was right. She called me and made me drive the crummy gas out of her car. It would sputter sometimes and actually die at stoplights. It did NOT like cheap gas. I still run the cheap stuff in my cars though.
That said, "octane" is another matter. Octane does not equate to quality. High octane means it the fuel is more resistant to burning. You do not want to use it in a lower compression engine that doesn't need it. If you do then you are giving up a bit of performance AND mileage. Not a lot but it's there. The old rule of thumb is to run the lowest octane fuel you can without your engine pinging. This is complicated by newer engine setups. In them if their fuel octane rating is too low they will simply retard the engine timing when ping or detonation is sensed with you none the wiser. Mostly. Run 87 octane in something like a supercharged Nissan Pathfinder that comes from the factory needing 93 octane and you WILL notice the lack of performance.
About the only way to prove you NEED higher octane is to monitor the OBD system while driving on that fuel. With a capable bi-directional scanner then you can see how on grades (most likely) the knock sensor is picking up detonation and the PCM is retarding the timing for you to prevent engine damage.
All vehicle manufacturers publish what octane fuel their vehicles require, in the owner's manual if nowhere else. Generally it is correct to follow that. At higher altitudes you can lower octane. In most of the country the lowest octane is 87. At "high" altitudes you will see 85 available. When you see 85 for sale is when you know you are high enough to make a change.
Some people run a higher octane to be "safe". Uusally because they have no idea what premium fuel actually is. To me that's just flushing money down the toilet.
As for additives, last I checked Chevron's Techron was the only one "approved" by Bosch. Been a while since I looked though. By the way, Bosch basically invented modern fuel injection so they kind of have a clue. Chevron fuels advertise that they already have Techron in them. However they don't qualify that. It might be one drop of additive per million gallons or something, we don't know. I have actually seen Techron help with some minor running issues related to "dirty" fuel injectors. I kind of like proof like that. I don't really use it much but you can bet there's a bottle of it in my garage. (Doesn't do diddly for carbureted engines though, unfortunately.)