I am trying to find out what kind of iPad I have so I can buy a case.

Try this

go here

https://checkcoverage.apple.com/

and enter your serial number. That’s the tiny print in the middle back or easier to read

settings

general

about

see if that gives you a model name

Identify your iPad model - Apple Support

As previously indicated, just touch the “M” model number on the About page - to reveal the “A” number.

Apple, perhaps confusingly, identify models with two numbers. Both numbers can be seen in Settings; just tap model number in About to see them both.

One number, prefixed with “A” is a generic model identifier. The other number, is an order number that identified the exact configuration (colour, internal storage, WiFi or WiFi & Cellular etc.) - this number will stand with one of four letters:

• M – Brand new device, meaning the device was purchased new
• F – Refurbished device, meaning the device has been through refurbishing process
• N – Replacement device, meaning the originally bought device was replaced by this model likely due to a service request
• P – Personalized device with engraving, meaning the device was customized with an engraving on purchase

I hope this clarification is helpful to you.

When you go to settings, general, about doesn’t it give you the model name of your device?

This is what mine looks like

It’s nothing secret. Several information fields work this way.

Try touching the software version - and it will reveal the software “build” version.

I hope the additional information has been helpful.