This is more of an "Amplitude Forums" ettiquete question than anything else.  

First, should ideas for the game be better posted in one place at a time?  i.e. In the design forum only or the "Ideas" section only

Second, if it's okay to post in both sections at the same time, is it better to post an idea in the design forum first, get it discussed and worked on, then post in "Ideas"?  Or would it be better to post in the "Ideas" section then post in forum, referencing the idea?

Well basically default sitation when you post a new idea is that nobody cares until you gain some traction.
Most people seek advantage by further cluttering the forum with reposting their idea links wherever they can.
Some of those people wear a VIP tag so I guess amplitude embraces such an action, thus do the same.

But logic remains the same, use ideas to outline and define an idea, then repost it in a forum post to make people aware. Even better if you have multiple ideas, simply maintain your own "look at me and my ideas thread".

Thank you for the info.  It does not fill me with much confidence in getting heard a whole lot better than other development companies but this is still better than most, even if only slightly by your posted experiences.

Compared to the typical forum process of "Noisiest Post Gets The Views", I do like the vote system that Amplitude has created here.  From those posts above, however, it seems that it only minimally works to encourage, and bring higher visibility, to the most popular ideas.  This is, of course, from the "users" perspective which is only what is available on the site.  The information about those posts might be available and visible in a different way to the Devs and employees of Amplitude so only they would know if it really makes a difference.

In any case, it still looks like the "louder" (see also: annoying, spammy, controversial, revolutionary, stellar, etc) individuals, topics, or ideas that are posted get the most attention in either location.  Additionally, in the "Ideas" section there does not appear to be any "cleanup" of those ideas which have been seen by Devs and moved to another section, so only those already highly visible and voted on ideas stay in the front and crowd out anything less than "super loud".

Until I see some change in the way things are currently sitting in the forum or Idea section I suppose I will have just try to be "loud enough" to be seen but avoid becoming annoying.

this particular post can show you how it's done ignoring the ideas framework completely, person posts an idea at the forum, which was probably posted as an idea before. At 30k G2G points gets dev response in 5 days and instant "gonna get that".
It's just that posting an idea gets lost in the rubble of reposts and posters rarely do their research on whether that idea is not already out there. You can easily spot up to 10 ideas that want "cross design retrofitting". It's just out of hand as frogsquadron states.
Just checking latest ideas, there are multiple people with broken english asking in ideas about alliance membership counts, and why they can't have an alliance in 1 v 1 or something like that.
That's the taste of it. Kinda like 9gag fresh section, but at least you can't downvote it and repost as your own. I bet there would be people capable of doing that.