Output data from computer to light up LEDs
An Arduino is surely a great choice if you are new to electronics in general.

You could also use an AVR/PIC micro controller with a USB to UART bridge (FTDI makes such devices, just google FT232 for example) to accomplish your task.

But I think for the first start I'd definitely go for the Arduino because of the following reasons:


It is incredible easy to use.
There are lots of pre-made libraries.
Great community and support.
Lots and lots of tutorials.
Well tested and established.
Easy and fast prototyping (you don't have to design your own PCB for example)
and... an Arduino is always handy to have regardless of experience level: it's a quick and easy way to test something out.


BTW

To give you a little start help:

You can use the pre-made Serial library to send and receive data from your computer.

Happy testing.