Definitely scout first.
Worker is often a good second choice, but since the good early tech orders are Pottery->Sailing/Calendar/Writing (assuming you want a chance at a wonder) depending on map, it's going to be a while before you worker can do too much other than build farms, so they become less important in a high food capital (though keep in mind that if you do go for an early wonder it'll be a while before you can get a worker out). On a map with a lot of land, a second scout is nice too: send 'em off in opposite directions and get twice the benefit. On water maps, an early trireme can be nice for exploration since almost everything is coast (for some reason) although they can't pick up ruins and escorting an embarked warrior (or scout, but warrior is better for taking out barb camps) is a bit tricky.
After the exploration phase, probably disband the scouts. They're useless after you have horsemen for all purposes other than blocking the other civs by plopping them on a choke-point hill.
For expansion, either you want to rush to Medieval (Civil Service or Compass, depending on whether you're on a water map), preferably by way of the Great Library (unless you've met Egypt, in which case don't bother trying for it) or a Great Scientist (if you're Babylon) and buy up the Patronage SPs before expanding (the extra food from maritime city-states = rapidly growth for new cities, so you'll catch up quickly) or you want to grab up the Liberty branch quickly (aim for the SP that gives all cities +1 culture) and start expanding ASAP.
Barbs are usually really stupid. If you leave a unit to fortify-until-healed, the barb will often times just pace back and forth next to the unit without attacking (unless it has another barb nearby to support it), so they're easy to take out if you pay attention to terrain. If you're having problems with them, consider adopting Honor (as it does have some military bonuses that are useful later on too), although it's among the weakest of the early game SP choices.
Edit: Actually, do try for the Great Library even if you meet Egypt, until you get to King.