The Opening Round
Since your opening build sets the tone for the while game, you should make sure that build is in line with your style of play. You have to build science ships to begin exploring your empire, but how many should you build? And should you build anything else or just those scis?
The conservative camp says that you should always build two science ships and nothing else, regardless of how many or how few jumps come off from your home world. This opening was Canon for years and only the most experienced dared try any other opening. The advantage of this build is that your tech development remains relatively high and you get to BR-2 faster. The main disadvantage is that if you have more than two jumps from your home world then they will not get explored for several rounds. Even if you send science ships down any new jumps rather than ones that were there when you first logged in, the cost of lost information is high (remember, "knowledge is power.") This is an especially important consideration in large games, where 3 and 4 jumps from home world is the rule rather than the exception.
A more aggressive approach is to overbuild your first turn. Here you build as many scis as you have jumps, plus possibly 1 or 2 colony ships as well. You can build up to a total of 5 (4 scis & 1 col, or 3 scis & 2 cols) and still have your scis at full strength the next turn so long as you don't build anything as they explore. This is a good approach for large games, because it gives the advantages of both early exploration and early colonization. It can be dangerous, though, in small games because your colony ships go out alone without protection from accompanying attack ships.
The ultra-conservative answer would be to build no science ships at all until you reach BR-2. This has the advantage of allowing your ships to plow over everybody else's BR-1s as they explore, but it has several down sides. First, building BR-2 ships with only your Home World's resources means that either you will have to build fewer ships, or your tech development will suffer. Second, you are several rounds behind in exploration, and if the other player has time to explore, colonize, and trick, he will be able to meet your scis with BR-2 ships of his own...and ones that were built with higher econ from a front line builder.