If you already have a pump you can carry with you, it's infinitely better than a CO2 cartridge since you can use it an infinite number of times, unlike CO2 cartridge that can be used only once.
As for what to carry, here's my set of tools: https://bicycles.stackexchange.com/a/71580/33932
...but you can go a long way with just tools to remove a wheel (Allen wrench if you have thru-axles), tire levers, patch kit, spare tube and pump. Add Park Tool TB-2 tire boots for sidewall damage, and maybe spoke wrench and chain tool plus chain pins or quick links depending on which you use to cover less likely but still common damage.
Note that most mini pumps are very slow. A fast pump would require unacceptably high force. One solution is a double action pump that pumps on both strokes (in and out) like Quickex Quicker Pro but those are no longer available. I think if I had to buy a pump today, I would buy a mini-pump with a hose that you pump agaist the ground to get more force.