I'm going to write a more simplified and generic answer about the process of answering the question, for people who have similar problems.
You list your goals as follows:
Confirm paper genealogy. Find 3rd/4th cousins to trade stories/photos. Find distant cousins to break through brick walls. Map Chromosomes and traits of individual ancestors. Preserve DNA data for future generations.
You don't have these goals ranked by priority. Doing that, and thinking about each one specifically, may help clarify which people you want to test in the future, and which ones you want to test right now.
For instance -- one goal is to preserve DNA data for future generations but that is broad, and gives you a reason to test everyone. It's important when you consider the terms and conditions of a specific testing company, e.g. how long might they store the samples of deceased relatives?
But if you want to consider preserving data and answering specific questions/confirming your paper trail in combination, the crucial point is this one:
Other than losing them, the real reason why they say to test the oldest first is you want to start a generation farther back. The extra generation means that they will on average match twice as much to each relative as the next generation will.
As previously discussed, to meet the goal Map Chromosomes and traits of individual ancestors. you could transfer AncestryDNA results to other companies or services such as GEDmatch which offer you a chromosome browser. To answer questions about specific traits, you could use Promethease
To decide where to use the remaining kit from FamilyTreeDNA -- I'm assuming this is their Family Finder (autosomal) test -- you could use the same reasoning as before (hold it in reserve for someone who can't take a spit test), or choose for another reason, like wanting to use their specific tools for a particular individual.
Roberta Estes' posts Which DNA Test is Best? from April 24, 2017 gives a snapshot of what tools were available at the time her post was written. When reading her post, or any other review (including our answers), it's crucial to keep in mind when the piece was written, since the DNA testing company 'landscape' is changing all the time. For instance as of April 2017 when Estes wrote her post, MyHeritage did not have a chromosome browser, but they have one now -- it was announced at RootsTech 2018.
To meet your goals Find 3rd/4th cousins to trade stories/photos. Find distant cousins to break through brick walls., you want to get yourself into as many testing pools as possible. Transferring test kits when possible is likely to be cheaper, and gives you a consistent data set across the platforms.
Answering the question of whether an individual should take tests from more than one company depends on what SNPs are tested at each company, and how much you want the data from that specific test. The additional information you might gain that way will be small and may not be cost-effective for your needs.
Just as any other question here, you can get better answers for yourself by narrowing down the question and making it more specific.
I highly recommend looking at the case studies of other genealogists who have combined paper trail genealogy and DNA, so you can see how they work. You can take a look at the DNA sessions from RootsTech by checking the 2018 Schedule and the RootsTech 2018 videos. Many genealogical societies have webinar series which offer free access to the public during the live broadcast -- you can find them by looking at the Geneawebinars calendar or other calendars of genealogy events.
Legacy Family Tree Webinars are available by subscription or by purchasing digital downloads of individual webinars. Each new webinar is free to the public for the initial broadcast, and the recording is free for the first seven days. Their webinar library includes a basic Foundations course of five webinars by Blaine Bettinger. They host the BCG webinars, and since the purchase of Legacy by MyHeritage, a series of webinars sponsored by MyHeritage. Usually the handouts for the webinars are members only, but check the BCG webinars in case the syllabus can be downloaded for free.
Of particular interest:
- Formulating a DNA Testing Plan by Blaine Bettinger, scheduled for Wednesday, March 28, 2018. He plans to talk about how to minimize costs while maximizing results.
- The Family DNA Project by Nicka Smith, scheduled for Friday, June 08, 2018, on creating and managing a DNA project for your family.
- Better Together: Making Your Case with Documents and DNA by Patti Lee Hobbs, CG, a BCG webinar scheduled for Tuesday, April 17, 2018, will talk about combining DNA evidence with the paper trail.
- Systematically Using Autosomal DNA Test Results to Help Break Through Genealogical Brick Walls by Tom Jones, PhD, CG, CGL, a BCG webinar presented on October 6, 2017, discusses a case study from the early 1800s.
- Avoiding Genetic Genealogy Pitfalls by Blaine Bettinger, presented on July 17, 2017, discussed the problems of not testing close relatives.
- MAXY DNA: Correlating mt-at-X-Y DNA with the GPS by Debbie Parker Wayne, CG, CGL, a BCG Webinar presented May 16, 2017, talks about correlating data from all the different test types with your paper trail research.
- Weaving DNA Test Results into a Proof Argument by Karen Stanbary, CG, a BCG webinar presented February 21, 2017, shows how to combine autosomal test results with paper trail research.
- FAN + GPS + DNA: The Problem-Solver's Great Trifecta by Elizabeth Shown Mills, a BCG webinar presented October 7, 2016, shows how to combine DNA results and the study of friends, associates, and neighbors.
Seeing the kinds of problems the professionals solve using DNA, and how they formulate a testing plan, is a huge help when you're struggling with making a testing plan of your own.