If you google "ffxiv error 601" you will see that it is an old problem going back years, with no obvious solution.
Usually you get that error when your bank (or someone) thinks there might be something fishy with the transaction and therefore blocks it. (Or browser problems, as mentioned.)
Wait a few days before you try it again. If that doesn't help wait a few weeks and try again - that helped me when I ran into this problem recently.