Its a matter of style and preference - personally I always go for the sandbox mode first as a way of learning the game as is.
Which ever way you go for it - learn the economy first and foremost, its the most critical part of the game (and frankly my reason for learning sandbox first). I started off playing literally only the first 12 game months or so, then restarting another game. That way I got inbto the economy and how it builds very quickly. The problem with not really getting into it fully, is you end up "firefighting" with all sorts of mayhem going on - and little time to properly learn all the other aspects of the game that you also need to learn. Take it all step by step, economy is the first step.
So learn economy first - its by far the most important aspect of the game - without it, the rest goes Bang, whatever clever tactics are employed. The best way to do that is dont build anything on planets (apart from the home world and one planet of PQ 10 or above to churn out colony ships) until population has reached the stage on each respective planet were its "in the green" in terms of income. Economy is affected by and helped a lot by economy structures etc etc - but its foundation is population, its vital to grow that as fast as you can in order that the economy can then be used to support other activities.
As to what those activities are, well, theres more suggestion on that than sand on a beach. However all such strategy and tactics are to no avail unless the economy is sound and roaring ahead. Its frustrating at first as you want to get into the whole "zap the aliens thing" - but it really is the best way to get going with this.
The classic phrase applies to this "the slow route is often the fastest route". Learn the economy and you'll quickly get to the stage of fleets wizzing everywhere etc etc, where we all want to be, try short cutting it by scimping the economy learning curve, and the game becomes the most frustrating nightmare on planet earth
Regards
Zy