595 series shift registers come in many flavors. SN74HC595 is the most usual. TPIC6B595 is similar but can be used with more power hungry applications. Pin layouts are different but they all operate in the same way.
I like to use various Arduino boards for AVR development. What I do not like are the Arduino libraries. They are often just wrappers around libc functions or rewrites of functions libc already provides.
Led matrices are fun toys. Who would not love blinkenlights? Electronics is hard. Electronics is much harder than programming. I had hard time trying to understand how do the led matrices work. What is best way to learn something? Build one yourself.