Think one of the reasons folks may choose not to respond or advise is simply due to the age of the code where you are beginning.
Some catch 22's when migrating the entire site ...
1. while users do come with the site migration ... what of any special authentications? Was password salt added to the 1.9.x? ... check config.php file of site.
2. plugins and addons ... they can stop an upgrade dead in it's tracks. Have you assessed those plugins ... gotta haves ... is there a compat version for any stage of the march.
Themes are a plugin ... they will change and have changed ... most recent version 3.7 introduces a major change ... why is that significant? Moodle is inline ... same interface for students/teachers as well as admins ... when/if it goes south, no one may be able to see/reach the moodle.
Advice ... stay with stock themes ... less trouble. But that comes from a person who is a minimalist - function over form.
3. any customized code?
4. legacy file system on the first hop from 1.9.x to 2.x ... can't get around it. Only new courses created in new versions of Moodle won't have 'legacy file system'.
5. 1.9 site use SCORM's? Major updates to courses there!
The stages in the march are necessary ... don't ask a very detailed why ... don't think anyone who is a developer or works for Moodle HQ will respond to that type of question.
Yes ... some major changes to DB ... and there are some persons getting trapped just from 3.5.x to 3.7 because of it.
Not only DB config, but DB version as well as PHP version ... at the right time ... can use PHP 7.0.x only after site is Moodle 3.0.highest.
If you choose to march ... hope you are using Linux. First thing I'd do is get the 1.9.x under git via side loading git ... that will result in upgrading the 1.9.x you have to the highest 1.9.x ... which along time ago has been the recommendation ... always update to the highest of the version you have before upgrading.
The other item ... backups ... at each stage ... a backup of code and a DB dump ... don't want to loose the ground you've gained if the next step in your march was one version to many, etc, or failed for some reason.
Now this is just me ... think I'd march to a supported version of Moodle .. for fixes (program as well as security). And as far as overall planning always try to shoot for long term support versions ... as quickly as you can to get the benefits of LTS.
There is an alternative to a march ... install of 3.7 via git (git makes it easy to update/upgrade later) .. and then try to restore no user backups from the 1.9.x .... that too one has to check plugins, etc.
So just about any way you go, there is no 'easy button' and it will require planning and research (pulling trigger on upgrading PHP at the right time ... or converting DB server and DB to supported character set/collation).
What OS is your 1.9 running under? Am thinking if the moodle is that old the OS might also be old ... and, shudder, hasn't been patched in many a moon. Wouldn't make sense to do this march on a CentOS 6 machine right about now ... EoL. Want a long term support version of OS as well.
How much memory/space, etc.?
Since you mentioned 'team' ... this server virtualized? On what/with what? VMWare? How many folks will be involved? Gotta true DB admin that knows MySQL or MariaDB? Big plus if you do! Any true programmers of PHP? Another big plus. Neither absolutely necessary but handy!
What of usage right now? Users number? How many courses? What's a ball park daily usage look like?
So there are also other factors as well.
Welcome the usual responders to jump in and add/take away from my 2 cents worth!
'spirit of sharing', Ken