stick with a medium map on the easiest difficulty -small and tiny are too unforgiving if you make a mistake, and the large and gigantic would make things too hard to keep track of if you are new.
at the beginning, colonize any planet with 15+ quality that you can get. dont worry about building any military ships -no one will attack you for quite a few turns. when the other AI's start harasing you by asking for money or whatnot, then start building your warships. you dont want your resource being wasted on attack and defense ships in the beggining when you dont even need them.
dont bother building any social improvements for the first few turns -you want all money going to military and research (to do this, go to your economics tab, and put your social all the way to 0% -remember to put the social back up when you start building social improvements later on).
when your colonizing phase starts slowing down, then you can start building social improvements. build anything that has no maintenece at first (soil enhancment, banking centers).
as for research, anything goes after you have researched universal translater and trade.