#4 - Make a Monk
In fact, make one character of every class. If you've been following Diablo III's development over the past few months, you've probably watched all the gameplay videos and have already decided which class you'll play first. You've probably also written off one or more classes as uninteresting based on the videos or ability details, but you might end up regretting your decision later. I had originally written off the Monk and the Demon Hunter based on their gameplay videos, but after playing them in the open beta weekend, I found my dismissal of them to be profoundly mistaken.
Feedback from the open beta weekend seems to agree, with a lot of players finding classes they had no interest in surprisingly fun to play despite earlier reservations. Blizzard spent a long time polishing all of the skills, so every class seems to be ridiculously fun to play. While it makes sense to concentrate on one character until you've explored the entire game, I highly recommend creating one character of each class and playing each for up to an hour before deciding which one to focus on.
#3 - Sell everything or feed it to the Blacksmith
Items are a big deal in Diablo III, especially as all spell damage is now based on weapon damage. The random drop chances can leave you with a pile of equipment you don't need while you're still stuck using an old weapon. Diablo III has solved this problem with a realm-wide auction house and crafted items that are competitive with dropped items. Break down any unwanted magic armour you find into crafting materials and use them to level up the Blacksmith artisan. The items he produces get random stats, so a lucky roll could produce items perfectly suited to a particular build.
Rather than break down any good weapons you find for materials, list them on the realm-wide auction house. People are sure to pay some serious gold for rare or high-damage weapons, as all skill damage is now based on weapon damage. Since everyone is starting out with no gold, there initially won't be a market for twinking characters. In the first few days, you should aim for realistic prices based on the amount of gold that someone of the item's level will have found. There's no sense asking for 100,000 gold for an awesome 10 weapon if most level 10 characters will have a fraction of that amount and the weapon will be obsolete by the time they can afford it.
#2 - Smash everything to bits
Diablo II fans will remember how the game instilled an almost compulsive desire to turn over every stone, kick open every barrel, and smash every pot in sight. Diablo III will feed that obsessive habit again, but this time you won't have to run up and open barrels manually. Skills can now be used to smash them, including ranged spells and area-effect abilities, so now you'll have no excuse to leave anything unsmashed. Anticipating players' destructive habits, Blizzard has even added destructible furniture and other objects that react with satisfying physics simulation.
There are achievements for destroying objects, and you'll even get bonus XP each time you destroy enough objects in a short space of time. Very few items dropped from barrels and other objects in the Diablo III beta, but this was only the start of normal mode and may even have been changed in the live game. I recommend smashing everything in sight as you play through the game, not just for the bonus XP, achievements, and satisfying physics collisions but also because we don't know what can drop from barrels and pots throughout the game.
#1 - Form a party
While there were lots of people who played Diablo II as a single-player game, it was always primarily a game about smashing through dungeons with a couple of mates. D3 will be much the same and has been designed with player cooperation in mind. Every class has one or two abilities that aid nearby allies, and Barbarians and Monks have abilities that buff or heal allies. Wizards, Witch Doctors and Demon Hunters can also spec out for massive damage if they know someone else will be keeping the monsters at arm's length.
If you want to tackle a certain quest with other players, you can set up a public game for that quest and other players can join in. You don't even have to be worried about someone stealing all the loot, as each player gets his own loot drop from every monster and boss kill. Playing with friends will increase the likelihood that at least one person will be able to use any good items that drop, and each member of a group will on average get more XP than a solo player. The only down-side is that parties are limited to four players.