pressing "Tab" will go around ships which have left over moves ...
Unless you set a ship or fleet to Guard or Sentry mode.
allthumbs, for a game like this, most folks develop a regular path through a given turn; different people will start by checking different things, but basically you want to be sure you've got ship production the way you want it, are building planetary improvements at a reasonable pace, and are happy with where your ships are stationed or where they're going. In the early game, your ship work will be about scouting the map and planting colonies; later, warships usually dominate the map.
But that's ineed a huge oversimplification. There are some threads around here that kind of work like strat guides, and the wiki is helpful, especially once you get to know the terminology of the game a bit better. I'd suggest that you just jump in the sandbox and start messing around. Even if you do very little other than clicking the Turn button, stuff will happen that should give you ideas about what you maybe should have done earlier or about what you might ask here on the forums.
Some tips I see regularly include:
- Keep an eye on how much you're spending--building too many improvements and ships too soon can break your economy; some players hardly ever rush-buy anything in the early game
- Remember to move your starting colony ship onto your homeworld so you can fill it completely; it starts out with 100 but can hold 250 (building population is the most important thing you can do to increase your income; larger starting pops grow faster)
- Consider upgrading your starting miner (if you're playing DA or TA) to another colony ship
Really, though, given that there are two expansions that both change the base game significantly and a very large set of basic game settings available, perhaps the best starting tip is to figure out which version you like best and what you enjoy in terms of the maps. The game is flexible enough that you can get something almost like a 'skirmish' mode on Tiny maps with very fast tech speed, and at the other end you can get a game that takes tens of hours to finish and has thousands of elements (ships, starbases, colonies) by the time its over.