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This is one of the common questions on this forum.
The brief answer is yes, IPad and a microphone goes a long way.
The most popular high quality microphone for apple products is the Apogee. It will only work with apple products.
Blue and Shure also produces some compact microphones that you can plug right into the lightning port.
I have the Shure MV5, which is not the most high end solution, but it works with both iPhone and with my PC through USB, and with my Android tablet through OnTheGo cable ( like any USB device will ).
If you read all the old threads you will find that an audio interface with its own power supply and a non- USB microphone will give you a higher quality, but it sounds like you want the compact easy solution.