I am by no means an expert, but I've only just started my city and have had great success to this point. For the record, $R is low residential, $$R is medium density, etc.
From a beginners stand point, I told myself I didn't want to build a SC2k "min/max" city like I used to. I watched the video in the OP to get a feel for organic city building (or at least a sample of it). It's not easy and requires more planning and patience than I expected, but I tried to start by plopping some wind power and building some farms and $R.
You can see the wind power in the picture and see how it expanded out. I've been building a LOT of farm land, and it's turned out to drive my $R and $$R demand up pretty high. You can see in the bottom left of my screenshot that I've built a little bit of $C, but only enough to meet the initial demand I had for it.
Once I started noticing $$R demand, I built a bridge across the waterway in my city and did a little $$R and $C. After demand for C dropped, I noticed I still had high demand for farms and $$I, so I built a small industrial park near the $$R settlement. You can't see that in my screenie because it's still VERY young and disorganized. I'll likely demo most of it and try again.
The biggest thing I've noticed is that you shouldn't worry about min/maxing your city. It sucks and takes a lot out of the creative building process. Also, I am playing on Easy because I like to see my developments happen quicker. I imagine I could be playing on Hard wit little to no issue at the current time. I have a positive income and haven't been too frugal with development. If I was more careful about placement and such, I'd be fine money wise.
Someone else has great (better) tips here I'm sure, but this is what I've got. It's been a LOT of fun just exploring the process and throwing stuff down. One thing I have to laugh at is how attentive I am to the layout of the city I live in right now. I've been paying attention to residential location in reference to commercial and industrial, the road patterns, and the density of everything. Very intriguing how that works!
Just a quick note, the $ signs aren't correlated to density at all. You can have $$$ Low-density development, and $ high-density development, and any other combination. (big mansions are an example of $$$ low-density Residential)