Here is a C-130 flight manual for reference.
This sequence started on A models because the GTC door had to be manually closed and the engine generators were split between inboard/outboard. So they would start #3 and #4 and then shut down GTC, manually close the door and then start left wing.
Some pubs mention starting engines in a different sequence than 3/4/2/1 to spread the wear and tear on engine starters. The first engine started off of GTC/APU Bleed air will wear faster than the others with engine bleed air because of the higher flow/pressure from the engines.
Generally speaking, if you 100% always start #3 first, data/trends say that you will replace the #3 engine starter before the other engines.