If you can muster the discipline, play each class up through some point, perhaps the Skelly King, before you move on. That way, you'll have a better idea about which characters will best fit your playing style. I headed into the beta thinking that the Barb was going to be great and the WD boring, but found it to be just the opposite.
Once you decide which character you wish to spend more time with, clear everything in each act in single player. This is actually the fastest way to get the money and experience you want.
Money is a bigger deal than it seemed to be in D2. Between leveling up the blacksmith and buying more stash space, I was low on funds most of the time.