Just so you know, right off, it's quite possible to play World of Warcraft over a 56k dialup connection.
You can get to level 50+ just like other new, casual players to the game.
It's possible to get into battlegrounds and (while being confused like all new players are) die over and over while also contributing to the death and mayhem against the opposing faction.
You can group up with others and tear through quests.
I'm sure you can do instances, but I haven't tested it myself - I'm just talking about the things that my father does while he plays this game we got him into just after Christmas time.
What I Do While On 56k Dial-up
I don't tend to play very much because if you're used to high speed, it CAN be a bit frustrating to deal with the overall feeling of slight lag.
So, I generally just load up my Auction House toon before I leave to come visit my parents (who live on the shore of a beautiful, sandy, clean lake so the 56k is only a slight inconvenience measured against serenity and beauty every day, every season), and every day I try to get onto WoW through Dad's computer, to cycle my auctions.
I've also made sure to log into my Alchemist to transmute a Primal Earth to Primal Life, since my Priest Healer will need a bunch of Primal Life for her Primal Mooncloth healing set at 70. Gotta keep the xmutes up on a daily basis if at all possible.
We've had some ISP problems this time around, however, so my WoW work has been a lot of video editing work, and not much Auction House work. Darn, a week away from home, unable to "play", and I only earned 1500g thanks to ISP problems.
Videos Edited This Trip
I've done a huge amount of video edit preparation and clean-up while visiting, figuring I would do most of the actual video development when I got home, but then the ISP problems have left us looking around at what to do "instead" of what we had originally planned (all of us in the family are very net-centric).
So, in all I've compiled three different Raid Boss Fight videos from footage I have from my play time, and I'm now at a coffee shop that has wireless internet, uploading them to WeGame.
Come back soon and they'll be linked :)