My Taiwanese friends reccomended me to keep my money at several banks, so if one has, ehem, any problems, you are still covered. Not much of a hassle.
There have been lots of problems with hacking and safety issues with Internet banking. For foreigners, the main problem is our ID number, which is slightly different from the locals’, and hence cannot be used in many instances.
By the way, you do have an ARC, right? Otherwise it is even more difficult -though not impossible. Just harder to open an account.
As to building credit, well, you need a credit card and that’s a whole different ball game. Search for the adventures, trials and tribulations in this department. I personally recommend getting an easy one, no local guarantor needed, and then build from there, unless you have relatives/friends/guanxi/lots of luck/a guarantor. There is a main office that will keep track of these transactions, and determines your credit score, not the bank.