first of all, welcome to CFC! i wanted to get that out now, since i tend to ramble and you certainly have permission to decide any of my posts are too long to read all the way through at any point
you have already discovered the best advice i can give you: go to the CFC website and forums! read some threads, ask questions, check out the "War Academy" link for some strategy articles (you can get there from the page you're reading this on by a dropdown box from "Civilization IV" in the Site Navigation bar at the very top).
when i was first learning i quite often did research in the order that was suggested (or almost), until i got a feeling for what techs are most useful for me. picking the recommended won't lead to "OMG i can't recover from this mistake i made back in 3300BC when i ought not to have listened to that stupid advisor!" at the lower difficulties so don't be afraid to do it while you're learning, even though the answer you'll get here is that most of us don't at this point. my research order now depends on many factors: my overall style, the map settings for that game, how many opponents i've met so far, etc. as you play, you'll learn more about your own style, and AI behavior, and your choices will change as you learn.
as far as the advice about what to build in cities, even if i know i'm going to build what the game is saying i ought to, i still hit 'examine the city' just to have a look around. just to remember what i have in there already, make sure the citizens are behaving themselves, etc. i 'micromanage' my cities, i like to do that, some people can't stand to spend the time doing it, and it's certainly not necessary to do it as often as i do, i'm crazy as you'll learn if you spend enough time here.
obviously you have already noticed that civ4 has a pretty steep learning curve in many areas. it's part of the reason the game has so much replayability and staying power for me and others, the complexity and flexibility of what you can do and how early decisions impact things far later, etc. some folks love that, some decide it's not their thing. i've never played RTS games (i call them click-fests, i'm just not a fast enough clicker to want to depend on my speed to win
plus i'm kind of, ummmmmmm, older than most of the RTS crowd which sure doesn't help the speed of my clicking ). maybe someone else here can compare how civ is different than RTS if that matters.