Hey! I've never built anything with Arduino, but ill soon order my first components and start building. I've been a programmer for many years.
So i want to build a "machine" that lets you input a sim card, send the phone number via wifi to my computer (or perhaps via cable? then the wifi module is not needed?)
I hope you know the phone number your SIM card corresponds to. What should be the advantage of having a device that tells you the phone number of an inserted SIM card?
The Uno and Sim900 can communicate, both ways, with the PC via the Serial Monitor of the Arduino IDE, so no need for wi-fi if your “machine” is near the PC.
If you want wifi or bluetooth to connect to the PC you have to do so via a separate serial link, but think you would be better taking the first route and proving that before trying wifi as well.
The Sim 900 and 800 chips only use the 2G network, some countries are ending 2G, so check which you have.
This is a good guide to setting up your Sim900 shield, but do check the jumper pin legends as they can vary from maker to maker.
There are software test /examples but quiet complicated for some ( like me), so have some very basic sms routines if stuck.