Do you remember when leaving the house involved remembering nothing more than keys, purse and phone? It's a distant memory for me after 4+ years of a never ending checklist of baby items I need. Our first trips out of the house with our oldest either had our poor little SUV loaded to the ceiling with tons of stuff we never used, or missed some very important items (forgetting wipes and a wet bag and ending up with a monster poopy bum was not a proud parenting moment!) With time, we figured out what we really needed, so I will pass on that wisdom to you!
The rule of thumb we followed when our kids were newborns is one diaper for every hour you will be away, plus one. As baby gets older, you'll get more of an idea of how many you need, but it is always better to have a couple extra just in case. If you are using a separate cover and insert system, having at least an extra cover or two is helpful in case the one they are wearing gets soiled.
You will develop your own list of what you find handy when out and about, This list also doesn't include feeding accessories, carriers, soothers etc. that you may need when out - just the stuff to cover your butt. Well, baby's butt.
If you are using cloth wipes, carrying some premoistened is handy in case you are doing a diaper change somewhere without access to water. We carry a tupperware container in our bag with a stack of damp wipes in it. You can also carry a bottle of whatever wipes solution you use and wet the wipes as you need them. AppleCheeks Wipes Solution is awesome for this purpose!