Another demo game. :lol
Here is what I got from so many begginings (obviously can't do a strategy guide with only 5 early games, but fuck it). I've been playing on Prince, btw.
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So, your only real first choices are Tradition or Liberty.
You either want a capital making lots of stuff fast (good for pursuing a cultural victory, since you will be focusing on snatching those wonders) or you want to spam settlers and expand fast, letting luxuries and cities-states with luxuries deal with the happiness burden, which is good for either a military, diplomatic (which is a kind of military/economic hybrid, because you will need an army to protect city states while bribing the hell out of them) or scientific victory. More ciities = more science. Maybe Ghandi is the exception to this since he can grow bigger cities, but lol no Ghandi on the demo.
So, chosing honor first just isn't worth it. You can already kill barbarians pretty easy with warriors. Another reason is just the timing of the great general, here I go into total especulation mode, but the games that I went honor first, that great general just stood there a lot doing nothing. Great generals are always useful, so you can delay that. What you can't delay are either the settlers (or you'll run out of land) or the wonders, because there is always someone snatching some wonder, it is really easy to be empty handed if you aren't focusing on that.
Another tip is that it is so motherfuckingly important to scout. Killing barbarians camp can easily give you enough money to get you an ally city state and the extra luxury can totally save your life if you are spamming settlers. (by spamming, I mean making a building, a unit then a settler. It's not really spamming, but it is enough to get you ahead of Prince A.I, at least on the conditions of the demo). Goody huts also give lot of culture sometimes and policies are game-changing. One new policy like Republic and suddenly you are building stuff so much faster. Or if you get a goody hut right at the beggining and give you culture, you can either increase production and grab a wonder right away or make a settler fast and get your second city out before everyone else. Every time you meet a new city-state they give you gold, too. 15 gold if they met someone before, 30 you they meet you first, so run around the map meeting them first is really good.
What I usually do is build a warrior first (so I have 2 barbarian killing scouts out there) then a worker, then a settler and from there, I start to go the direction of the victory I want to pursue. This seems to work better than making a worker first (one lonely warrior scout is too little and before you get some techs, you really don't have that much to do with the worker), I actually never built a scout, so who knows? Maybe saving those turns can be good, I don't know, having something that can actually kill barbarian seem better.
Anyway, this could be completely wrong, what do I know? 1 day and 17 hours before I can know what the real game is like and maybe make sense of this motherfucking wall of text I just wrote at 4 am.