Well, depends on the LEDs.
Partycat is very much meant to work with one string of ws2812 LEDs (or ones that use the same protocol) and a string of other LEDs, through the mosfet.
So, if you wanna go that route (which I suggest), grab https://www.adafruit.com/product/1734 or https://www.adafruit.com/product/1938 (8 or 5 mm WS2812 LEDs), and hook them up to the partycat. This will allow you to do a bunch of great patterns on the outside rings.
Then get central LED like this: https://www.adafruit.com/product/518, or something similar (maybe even brighter if you want to be able to light up a room, or a soccer field)
Don't necessarily order from adafruit. They aren't the cheapest, but they do have great quality and customer support.
Lots of people here will be able to help with partycat and programming.
One more thing: Think about an input, like a button, to change patterns. (This CAN be your phone, as the partycat is wifi enabled)
Also think about where you'll be providing power.