Good tyres will reduce the probability of punctures. Unless your racing, I would recommend at a minimum getting some 25mm Gatorskins. 25mm have also been scientifically proven to be faster than 23mm as they deform less.
To reinflate the punctured tube.
2 Inner tubes
Personally I have not found patches to very good. At best they can get you home, but haven’t found them useful beyond 5 miles. If you have space carry 2, but minimum 1. They are relatively cheap, and hoepfully with good tyres and pothole awareness, you will rarely need to use them. Keep the tubes wrapped in a carrier bag/plastic to protect from damage.
To help you remove the tyre quickly. If your starting out carry 3 to be safe. As you get more confident, you’ll be able to get away with 1.
For when you are having one of those days / rides. They will allow you to get home even if you have stop occassionally to reinfalte. have you noticed I like redundencies.
With the exception of the pump I’ve been able to fit all of this into frame bag, which stays in the bottom of my rucksack.