Newbie wanting to create a DIY LED pixel matrix


I am a complete newbie to working with electronics, let alone LEDs, but I've done a little reading up for a few days.

I would like to create an LED matrix in the cheapest way possible. Ideally what I would like is to be able to have it display pictures at the push of a button, perhaps with a default cycle running until the button is pressed.

I was thinking this is best done with pixel lights popped into foam core in a snake pattern.

What I would like to know is where to get started. I saw that Arduino sells a starter kit. Is that best to just introduce me to the concepts?

I know I'll need to be programming and have seen Adafruit_NeoMatrix and Adafruit_GFX mentioned.

I guess I'm wondering how long this will reasonably take me to learn and create and if I can do it within a reasonable budget. Where would you start a newbie?