i wouldn't aim for culture right away. i really like it but it has some nuances that might be confusing for a beginner, and more importantly would give you bad habits as far as trying those things in a 'normal' game since it's completely different.
as far as military and space race (and diplomatic/UN), you don't necessarily have to decide before the game. if you leave multiple victory conditions on (meaning the boxes are checked), you can see how the game progresses and which looks more doable as it goes on. since you're looking for the easiest type (a good idea as a beginner!) i'd leave those all as options.
there are 2 types of military victories, most folks end up preferring one or the other. domination requires you to control a certain percentage of the population and land mass, which means you can win by elimnating most of the bad guys but some still live. conquest means they ALL have to die. conquest clearly takes more time, but gives some bloodthirsty folks more satisfaction. that one you do have to decide between before you start the game pretty much. unless the civs are spaced in the right way, and you are careful to raze most cities rather than capture them, and not make too many of your own, it's possible to hit the domination condition by accident before the conquest condition. as a beginner i'd suggest not limiting yourself to only conquest until you find out just how much punishment you like to inflict on the bad guys
one thing i'd do as a beginner is to NOT check the 'require complete kills' box. with that off (not checked), once you kill a civ's last city they're gone forever. if you have that on, you often have to hunt down one or two units they have out there skulking around which can be oh so frustrating.
that's advice for before you ever start the game. even if you do ultimately win by space race, you probably aren't going to let everybody live happily ever after so you'll be in some wars either way. if you were looking for tips about how to win a certain way, well, i'm not the best source for those. in fact, since you asked for pros to tell you, i ought to warn you i ain't one, so take everything i say with a grain of salt.
have you read the articles in the
War Academy yet? there's some great advice there.