How to input content items in the dashboard and pull them out into web pages?

(I posted this question also here, with an image of a wireframe)

I’m designing a website for a municipality-owned company that facilitates local entrepreneurs. Here’s my WP install in development: http://masekpro.salab.im

I’ve made wireframes for all pages, here: https://www.dropbox.com/sh/369cveq5n9tkjkb/-6V3dkMMDT
(things keep moving, so they are not perfectly up-to-date, but the main features are there)

I’ll have a 1st-level navigation menu with 9 pages, one of which is a blog-type news index (“Ajankohtaiset”).

Most of the other 8 pages and their 2nd-level sub-pages will be fairly straighforward, relatively static pages. I’ll develop a couple of page templates to accommodate their layouts.

There will be several “boxes” with text and/or images and/or links, to be pulled in by various page templates. For example, the home page (“Etusivu”) will have 5 such boxes at about ⅓ the page width each, and a map at ⅔ the page width.

(1) So my first question is:
How do I best create the input functionality for those boxes on the editor’s dashboard?

Should I input their content simply in “pages” on the dashboard?
Should I create custom pages, i.e. special page templates?
Should I create custom post types?
Should I create some other kind of input forms?
Should I build widgets for this purpose? If so, how?
Any better ideas?

The idea is that it works well, technically, but also that it will be easy for my customer to update information in those boxes.

If the purpose of page templates is only to vary the layout of web pages, then I suppose they are not the way to go.

Custom post types sounds logical, but aren’t “posts” meant for reverse-chronological entries? Chronology is not relevant to these boxes. Or should it be?

(2) My second question relates to creating 3 collections of simple database records (“companies”, “office space” and “building lots”) and pulling them into pages as lists (all; within a category; or as search results) with thumbnails and a few lines of text with a link.

So, again, how do I create the input functionality?

Regular pages?
Custom pages templates?
Custom post types?
Custom input forms?
Widgets?
Something else?

Much appreciated!