Anyewo,
A lot depends on your company procedures. As I recall, the Boeing advice was not to fly in Vertical Speed mode if the throttles go to idle - however this is exactly what you need to do to control exactly the path using the method above. If you watch your level offs carefully it's not a problem but check first what the company thinks.
Even if you use the FMC based descent, have your own calculations going as a cross-check - very useful if you are suddenly sent direct to somewhere, or if the controller asks "can you make FL50 by a certain point?"
In my experience the 737 FMC - certainly on the older FMC models would vary the ROD a lot, which makes any kind of follow up very difficult.
The 737 is normally a 3deg descender - you have to be quite light or use speedbrakes (which are not very effective) to get more but the cabin altitude system is not a problem so you can use 3 deg from the top of descent. Plan on 3 and then the speedbrakes are a back up if you need more rate. Lower down, the gear is a great help in getting height off - the Flaps/Slats have, as you know quite low limiting speeds and cannot be used for this purpose. Enjoy, Few
