The max per character is a signed 32 bit integer, ((2^31)-1) 2,147,483,647 or 214,748 gold, 36 silver, 47 copper. I can confirm this from personal experience, though I guess the guildbanks use a bigger datatype (or a non signed 32bit int)
yes, gbank required.
a single char can bring with himself max 214k.
gbank limit is higher.

GM's ingame ticket confirmed gbank is the way to store in same place 1000k or more.
no sure infos about gbank limitation.
time ago found a post in wow europe forum about a player hitted same amount (he did playing with ah in over 400 days): in that post someone said gbank limit is 64 bit value, other 32 bit -unsigned.

qana, my rogue, managed 70/80% of ah activities: previously i used another character.
Player stats, gold acquired values, are regular 32 bit - signed.
i can confirm, at 214k, qana stats jump in negative, losing values format.
after a bit of time, probably after other 214k acquired, qana stats values back in positive and format was back and ok. and then again negative values, again format lost.