As others have said, don't worry about running your slider low if it means you can get more land. You're basically sacrificing short term tech for long term tech and production. So long as you can get writing and pottery before your units begin striking, you should be fine. Of course, building enough workers makes all the difference.
After that, the most important economic techs are usually, in order, Alphabet (to trade and build research), Monarchy (to grow your cities so they can actually use their land), Currency, and Code of Laws. You may also want Iron working if you need to clear jungle, but you can usually trade for it. Once you have those techs, you can pretty much expand as much as you want indefinitely.
Diplomacy-wise, check out
this thread for a handy chart that tells you when the AI will declare on you. The interesting part of the chart is the NoWarProbs, which are the probabilities that an AI will choose NOT to go to war with someone, after they have rolled the dice that tells them to look to start a war. Every AI leader has a set for every disposition. For example, Gandi's are 20(Annoyed), 70(Cautious), 100(Pleased), and 100(Friendly). This means Gandi is very likely to declare at Annoyed, reasonably likely at Cautious, but will never declare at Pleased or Friendly. Granted, Gandi doesn't roll the dice to start planning a war very often anyway, but knowing that, say, Napoleon will declare at Pleased, but Ramesses won't, is very useful!
A word on demands for tech or gold: Many of the AI have a chance of declaring if you refuse a this type of demand, even if they are at a disposition that they wouldn't declare otherwise. The upshot is that you should almost always bend over to people you are legitimately scared of, so long as it's not a crucial tech. Heck, bend over to everybody you want to be your friend, as well. That +1 diplo bonus helps a lot.
