Is my idea for a two motor controlled device possible?

Hello, I am just staring to use arduino stuff and was wondering if my idea was even possible. I want to make a device that will be able move in a grid, similar to a cnc machine, minus the z axis. While also having, say five different patterns the device executes, without having to reprogram it, just pushing a button out of five buttons. My concern is the amount of memory the arduino uno has. Is it possible there is enough memory as is, or is there anyway to add an external storage that the arduino reads from? I'm sure the actual size of the code for the different functions has an impact but I haven't learned enough yet to know how big that sort of code could be. Any help is greatly appreciated!

I recommend you writing code, compile to see how big it is. And then compare with Memory of Arduino Uno. If not enough, compare with Arduino Mega.
I guess that at least Mega has enough memory for your application

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